Submitting errata

If you notice any mistakes in the book, big or small, please send an email to the author at weissman AT ucsc DOT edu.

Please include the subject line ERRATUM (or ERRATA if plural, I guess!).

Before submitting your erratum, please look through the list below to see if it has already been caught.

When submitting errata, please include the following information:

All accepted errata will be acknowledged on this page, and also in future editions of the text. Thank you to all the colleagues and students who caught errata before the first edition was published! Thank you to Spencer Martin, at Cleveland State University, who found the first post-publication erratum. Thank you to Dr. Paul Stanford, at the University of Texas, Dallas, who found around 30 errata (!) and made excellent suggestions which I hope will be incorporated into the second edition someday. Thanks to Corey Shanbrom for finding dozens of errata and typos, even the tiny ones. Thanks to Vens Lee for correcting the French accents. Thanks to Claus Sorensen and Erik Wallace for providing corrections and constructive feedback after teaching with the book.

Current errata (mathematical errors in red)

Preface
Page xii
The formula |xy| ≥ |y| is strangely mis-duplicated as |xy| ≥ |x| on the line below. (Thanks to Terry Michaels, October 2018.)
Chapter 0: Seeing arithmetic
Page 1 (darnit)
The word "myred" should be "red". Long story on this one: You might notice that some red text/dots in the text are more orange-ish than red. The reason is that screen-red (RGB) looks orange when printed. I thought I took care of this by creating a good print-red (in CMYK colorspace) which I called "myred". Indeed, I changed lots of red to "myred". But I missed some dots and text. And I accidentally changed the word "red" to "myred" on page 1. Whoops.

Page 3

The stacking-corners diagram is 13+1 dots by 13+1 dots, but the labels suggest that it is 14+1 dots by 14+1 dots. (Thanks to Spencer Martin, August 2017.)
Page 5
Marginnote, top-right: Zero is also typically considered a triangular number.
Page 7
Marginnote, first sentence: "triangles" should be "triangle". (Thanks to Chris Shelley, November 2017.)
Page 7
Paragraph below the big figure: Delete "on" in "Add only on..." (Thanks to Conner Jure, January 2018.)
Page 9
Just above Prop 0.13: "are form a" should be "are from a".
Page 11
First two paragraphs: The first paragraph discusses 8039, and the second paragraph discusses 8093, a strange and possibly confusing shift. (Thanks to Kristyn Bucci, April 2019.)
Page 14
Line 4: "they becomes second nature" should be "they become second nature". (Thanks to Erik Wallace, January 2018.)
Page 15
Line 5: "accesory" should be "accessory". (Thanks to Terry Michaels, October 2018.)
Page 16
Line 2: "analagous" should be "analogous". (Thanks to Alberto Trombetta, January 2018.)
Page 16
The end-of-proof square comes a few lines too early in Proposition 0.27.
Page 16
Last line: "mutliple" should be "multiple". (Thanks to Alberto Trombetta, January 2018.)
Page 18-19
There is a spelling mistake, and a few missing diacritic marks. Ganipāda should be Gaṇitapāda (the "ta" is missing, also the dot below the n). Twice, Āryabhata should be Āryabhaṭa (a dot below the ṭ). Aryabhatiyabhasya of Nilakantha should probably be Āryabhaṭīyabhāṣya of Nīlakaṇṭha. (Thanks to Shreevatsa R, December 2018.)
Page 21
Exercise 24: By "When is T(N) even?" please understand "For which values of N is T(N) even?". (Thanks to Erik Wallace, January 2018.)

Page 21

Exercise 26: 6N should be 6 S(N). Also "perfect squares" should be called "squares". (Thanks to Patrick McDonald, January 2018.)
Page 21
Exercise 27: The parenthesis ) should be removed after "Notes". (Thanks to Chris Shelley, November 2017.)

Part I: Foundations

Chapter 1: The Euclidean algorithm
Page 25
Line 4: Should commas go inside quotes or outside? It depends on whether you follow American or British conventions. Here they're inside. Elsewhere, they might be outside. This will require a whole-book search and replace for consistency! (Thanks to Alberto Trombetta, September 2018.)
Page 29
Problem 1.5: Line marked (Step 3). The number 4460 should be 4640, at the end of the inequality. (Thanks to Ashelee Collier, February 2020.)
Page 29
Proposition 1.6: The end-of-proof square is missing. (Thanks to Vens Lee, February 2019.)
Page 34
Line 13: "equaions" should be "equation".

Page 36

Proposition 1.20: The integers a,b should both be nonzero.
Page 36
Proposition 1.20: The end-of-proof box is missing. At the end of the proof, the reader may verify that the given u,v are solutions of the equation au + bv = 0 for every n. (Thanks to Andrés Eduardo Caicedo, January 2017.)

Page 36

Theorem 1.21: The integers a,b should both be nonzero here too! The Theorem almost works when one (a or b) is zero, but not quite at the end. (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 39
The end-of-proof (QED) square is misplaced. It should be just above Problem 1.24.

Page 40

Corollary 1.25: The integers a,b should both be nonzero here too. (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 41
Proposition 1.27 and Corollary 1.29: The end-of-proof boxes are missing. (Thanks to Erik Wallace, January 2018.)
Page 43
Quote from Bézout: "on peut 542 livres" should be "on peut payer 542 livres." (Thanks to Ashelee Collier, February 2020.)

**Page 45**

Exercise 14: The last line should read "LCM(u^2, v^2) = LCM(u,v)^2". The final "squared" was forgotten.
Page 45
Exercise 19: The word "same" is missing, and the last line should read "look (geometrically) the same right-side-up". (Thanks to Jeffrey S. Haemer, January 2018.)

Page 45

Exercise 21: The question "How often...?" should be made more precise. If the tortoise begins jogging at time zero, describe all of the times at which the tortoise and hare cross paths (assuming they run forever at the same pace). (Thanks to Erik Wallace, January 2018.)
Chapter 2: Prime factorization
Page 49
Marginnote: A primality certificate typically refers to something more than we've described: a specific theorem and relevant parameters that rapidly guarantee primality.
Page 51
Figure 2.1, Marginnote: The record has been broken! News about the newest and largest Mersenne prime can be found at the homepage of the Great Internet Mersenne Prime Search. (Thanks to Andrés Eduardo Caicedo, January 2017.)
Page 53
The appearance of Li(x) and li(x) may be confusing. Li(x) is defined on the page, as the integral from 2 to x of (1 / log(t)) dt. The function li(x) is the integral from 0 to x of (1 / log(t)) dt. But this integral is a bit subtle due to the singularity of 1 / log(t) at t=1. The integral defining li(x) should be interpreted as the principal value. Or one may forget about this difficulty, and define li(x) to be Li(x) plus a constant, as in the footnote on this page. (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 54
Theorem 2.11 should really be attributed to Zhang-Maynard-PolyMath, as explained in the Historical Notes on p.71. (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 57
The exponent of 7 should be called f_7, and not f_5, in equations (2.1), (2.2), and (2.3).
Page 57
Last paragraph: For the proof of existence of prime decomposition, look back to page 48. (Thanks to Erik Wallace, February 2018.)
Page 58
Problem 2.16: The problem is missing its end-of-problem check mark. (Thanks to Corey Shanbrom, February 2019.)
Page 62
Sidenote 19: Change "has" to "as" in "do not have 2 has a common factor". (Thanks to Jeffrey S. Haemer, January 2018.)
Page 63
Line 3: change "generators" to "generates". (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 63
Theorem 2.28: The proof is missing its end-of-proof box. (Thanks to Harrison Henningsen, February, 2018.)
Page 64
The reference for Jacobi's four-square and eight-square theorems is C.G.J. Jacobi, Fundamenta nove theoriae functionum ellipticarum, Königsberg (1829). (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 65
Theorem 2.3.1: Here it seems that I call them divisor-power-sums, and earlier, I call them divisor-sums. A single choice should be made for consistency. (Thanks to Corey Shanbrom, February 2019.)
Page 68
A period wandered away from 2N, at the bottom of the page.
Page 69
An update: by a 2015 paper of Pace P. Nielsen, it is now known that an odd perfect number must have at least 10 distinct prime factors, (Thanks to Andrés Eduardo Caicedo, December 2017.)

Page 71

In Footnote 40, the statement li(n) - Li(n) = log(2) is false. Instead, this should be li(n) - Li(n) = li(2), and li(2) is approximately 1.045, as stated in Footnote 8 on p.53. (Thanks to Andrés Eduardo Caicedo, December 2017.)
Page 72
Exercise 1: The first "and" should be deleted. (Thanks to Jeffrey S. Haemer, January 2018.)
Page 72
Exercises 1,2: The factorial is defined in Exercise 2, but also mentioned in Exercise 1. (Thanks to Corey Shanbrom, February 2019.)
Page 72
Exercise 3(b): Every element of T *greater than 1* can be factored as a product of irreducible elements. Or, you can read this as some mathematicians would, noting that 1 equals the "empty product". (Thanks to Jeffrey S. Haemer, January 2018.)
Page 72
Exercise 5(c): A period is missing. (Thanks to Corey Shanbrom, February 2019.)

Page 73

Exercise 17: One must require n > 1 for this construction of amicable numbers to work! (Thanks to Andrés Eduardo Caicedo, January 2017.)
Page 73
Exercise 15: The dash (before "n is even") is not a minus sign. Change this to "Hint: consider the two cases where n is even or n is odd." (Thanks to Corey Shanbrom, February 2019.)
Page 73
Exercise 18(b): The period should go within the parenthesis at the end.
Chapter 3: Rational and constructible numbers
Page 76
Marginnote above figure: Change "one associate" to "one can associate". (Thanks to Andrés Eduardo Caicedo, January 2017.)
Page 76
Marginnote 3: Change "from" to "and" in "...both 1/0 from -1/0...". (Thanks to Harrison Henningsen, February, 2018.)
Page 80
Marginnote 13: The "line between them" does not make sense if the circles are concentric. If you wish to play with the circles and lines, Desmos is a good free tool. Here's a Desmos graph with sliders to control the circle and see where the line goes. (Thanks to Jeffrey S. Haemer, February 2018).
Page 80
An end-of-proof box is missing at the bottom of the page. (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 81

Middle of page: "Expanding and multiplying through by cd" should be "expanding and multiplying through by c^2 d^2." (Thanks to Jeffrey S. Haemer, February 2018.)

Page 81

Ten lines from the bottom, the x^2 + y^2 should be a u^2 + v^2. (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 81

Sidenote 16: u should be a/c (not a/b) and v should be b/c. (Thanks to Jeffrey S. Haemer, February 2018.)
Page 82
Second paragraph, delete "must" in "must would". (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 83

Theorem 3.8 (Rational Root Theorem): The constants c0, ..., cd do not have to be positive, and in many important examples, they won't be! (Thanks to Junecue Suh, January 2018.)
Page 87
Figure 3.10, marginnote: The Ford circle at 7/3 is not depicted; instead the circle at the non-reduced fraction 4/2 is depicted, which sadly does not osculate any other circles. (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 88

Theorem 3.15: One must assume that the rational numbers a/b and c/d are distinct for the proof to go through as written. (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 90

Figure 3.15, marginnote: In fact, bx is not equal to 1. Place x within an absolute value: b |x| = 1. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 90
Proposition 3.18: A remark... the proof only considers the Diophantine equation ay - bx = 1, whereas kissing fractions also arise from solutions to ay - bx = -1. But (x,y) is a solution to the first equation if and only if (-x, -y) is a solution to the second equation, and both (x,y) and (-x,-y) produce the same rational number y/x. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Pages 90-95
I really should have mentioned Farey sequences by name, and in the historical notes.
Page 94
Lines 3-4: There must be a clearer way to write this, rather than "to bear results on". (Thanks to Pete Morcos, October 2019.)
Page 94
Last line: Oops.. it should read that the margin is too small to contain the proof, not that the proof is not too small to fit in the margin! Apologies to Fermat and Mr. Barnes, my high-school Latin teacher. (Thanks to Harrison Henningsen, February, 2018.)
Page 95
Sidenote 41: "...on can try..." should be "...one can try..."

Page 96

Exercise 2: The triples (x,y,z) should be required to be pairwise coprime, i.e. GCD(x,y) = GCD(y,z) = GCD(x,z) = 1. Otherwise a single triple easily yields infinitely many by scaling. (Thanks to Steven Gubkin, October 2017)

Page 96

Exercise 6(b): The variables a and b got switched. It should read "the equation ax+by = 1 implies xπ/b + yπ/a = 1/ab." Also, there's an extra period in "cosine.." (Thanks to Jeffrey S. Haemer, April 2018.)

Page 97

Exercise 9: Sadly, no fraction kisses 77/133. Change 133 to 138 for a better problem. (Thanks to Jeffrey S. Haemer, April 2018.)
Page 97
Exercise 11: The word "adjacent" means "tangent" here. (Thanks to Patrick McDonald, March 2018.)

Page 97

Exercise 13: The number x should be irrational throughout! (Thanks to Patrick McDonald, March 2018.)
Chapter 4: Gaussian and Eisenstein integers
Page 98
The Gauss-inert and Eisenstein-inert primes are mean to be highlighted in blue. But perhaps they look black in print. This image needs some color-tuning.

Page 99

Sidenote: For the explanation to make sense, "integral domain" should have been defined. An "integral domain" is a ring in which xy = 0 implies x=0 or y=0.
Pages 101, 102
Problems 4.2 and 4.4: the word "Solution" and the end-of-solution checkmark are missing. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 106
Line three: "centered z" should be "centered at z."
Page 108
Theorem 4.11: "or side length |b|" should be "of side length |b|". (Thanks to Corey Shanbrom, February 2019.)

Page 109

Five lines from the bottom: (-2-i) should be (-2+i), in the second line of the Euclidean algorithm. (Thanks to John McHugh, July 2019.)

Page 112

Margin-figure 4.17: The figure labels the points correctly, but the caption misidentifies some of the points. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 113
Top sidenote: The word "correspond" is misspelled. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 114
Theorem 4.18: In the second line of the proof, "Therefore" is misspelled. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 115
Figure 4.25, Caption: "above the Eisenstein primes" should be "above the prime numbers". (Thanks to Pete Morcos, October 2019.)
Page 116
Proposition 4.22: The proof is missing its end-of-proof square. (Thanks to Corey Shanbrom, February 2019.)

Pages 116,117

Both margin-figures: A sad decimal-to-percent error occurred. The axis ticks should be labeled by 49.8%, 50%, and 50.2%. (Thanks to Samuel Wagstaff, December 2017.) Also, note that (on p.116) the 25444 split primes and 25436 inert primes is not an error -- at that point in the graph, the number of split primes (barely) exceeds the number of inert primes.

Page 117

Proof of Proposition 4.26. The q=x+yi should be a q=x+yω, near the end of the proof. (Thanks to Samuel Wagstaff, December 2017)
Page 118-119
The blue dots represent the primes of type (S), i.e. split primes. Also, the remarks on p.118 about the black ticks applies equally well to the figure on p.119. (Thanks to Corey Shanbrom, February 2019.)
Page 123
Sidenote: In the phrase "there are infinitely many Gaussian prime numbers of the form x + i," the variable "x" is meant to refer to an ordinary integer (as in the exercise), not a Gaussian integer.
Page 123
Exercise 16: The grid of parallelograms is really a grid of squares. (Thanks to Claus Sorensen, February 2019.)

Part II: Modular Arithmetic

Chapter 5: The modular worlds
Page 130
The modulus does not really need to be positive, for almost everything we do. Congruence modulo a negative m is the same as congruence modulo its absolute value. In fact, one can allow congruence "mod 0" too, which is just the same as equality!
Page 138
A stray equal sign appeared, in the first centered equation. There should just be a congruence, so m is congruent to 0 mod m at the end.
Page 141
Last two paragraphs: When writing about "two roots", I mean "two distinct roots". For more on Cebotarev's Theorem, see Stevenhagen, P. and Lenstra, H. W., Jr., "Chebotarëv and his density theorem", Math. Intelligencer 18 (1996), no. 2, 26–37. (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 141

Problem 5.27: The end should read, "The solutions are x ≡ 2 mod 7 [not 3 mod 7] and x ≡ 5 mod 7." (Thanks to Samuel Wagstaff and Robert Woodley, December 2017)

Page 143

Proof of Proposition 5.31: It doesn't make sense here to say "both A and B are positive integers." Replace it by "both A and B are nonzero." (Thanks to Erik Wallace, April 2018.)

Page 144

Line 3 and line 8. The subscripts (1 and 2) migrated outside the absolute value. Please put them back in, next to the letter R where they belong.
Page 145
Mid-page: "Linear polynomials play a special role." They do not "place" a special role.
Page 146
Line 8: "degree up to 19" should be "degree up to 20".
Page 146
Just above Theorem 5.41: Change "approximation" to "approximation is". (Thanks to Pete Morcos, October 2019.)

Page 146

Line 14: The integral should have upper-limit x, and not infinity. Its limits should match the sum. (Thanks to Adrian Shestakov, March 2018.)
Page 146
In mentioning the Riemann Hypothesis, I used "big-O" notation without definition. To clarify, the Riemann Hypothesis states that the absolute error is bounded by some constant, multiplied by the square root of x, multiplied by the logarithm of x. (Thanks to Corey Shanbrom, February 2019.)
Page 149
Some accent marks are missing from the French. It should read "Premièrement, tout nombre est composé d’autant de quarrés entiers qu’il a d’unités". Note this is based on the cited edition of Tannery, and may differ from other published editions of Fermat's letters. (Thanks to Andrés Eduardo Caicedo, January 2018.)
Page 149
A French typo, mid-page: "méthods" should be "méthodes." (Thanks to Vens Lee, February 2019.)
Page 149
The cited 1828 paper of Jacobi is really an announcement, and not a sketch of the proof (as suggested in the sidenote). (Thanks to Andrés Eduardo Caicedo, January 2018.)

Page 150

Exercise 5: One should assume that m is nonzero. Perhaps even that m is positive, if you don't like negative moduli.
Page 151
Exercise 16: Here, I do not capitalize after the word "Hint:". Elsewhere, I do capitalize. I should be consistent. (Thanks to Corey Shanbrom, February 2019.)
Chapter 6: Modular dynamics
Page 152
In the opening figure, there's a strange isolated semicolon floating around the bottom-left.

Page 154

In Problem 6.1, there are 7 equal signs that should be congruences instead.

Page 157

Figure 6.6: On the right, 11 and 13 should be swapped. Oops! (Thanks to Anne Trainor, April 2019.)
Page 161
In Problem 6.19, the binary is strangely missing for the exponent e=4. The binary should be b 100. (Thanks to Jeffrey S. Haemer, May 2018.)
Page 163
Figure 6.9: The caption should read "mod 41041" and not "mod 667." (Thanks to Corey Shanbrom, February 2019.)
Page 166
In sidenote 7, "precient" should be "prescient". (Thanks to Alberto Trombetta, September 2017.)
Page 166
In sidenote 7, "laying the" should be "laying out the". (Thanks to Pete Morcos, October 2019.)
Page 167
In the centered equation, the last "=" should be a congruence (mod p). (Thanks to Corey Shanbrom, February 2019.)

Page 170

In Exercise 7, one should assume a > 2 and b > 2 for everything to work out correctly. (Thanks to Jeffrey S. Haemer, May 2018, and Mohit Gurumukhani, November 2018.)
Chapter 7: Assembling the modular worlds
Page 174
Just below triple equation: "if it were fewer than 100" should be "if 128 were not greater than 100." (Thanks to Pete Morcos, October 2019.)

Page 177

Marginnote 2: At the end, u should be between 0 and d, and v should be between 0 and e. (Thanks to Sophie Larsen, November 2018.)
Page 178
Top of page: "Chinese Remainder Theorem" should be capitalized consistently throughout the book (Thanks to Corey Shanbrom, March 2019.)
Page 187
Line 3: The equality should be a congruence. (Thanks to Corey Shanbrom, March 2019.)

Page 190

Exercise 13: In part (a), |x|p can certainly equal 1, even when x is not 1 or -1. (see the example above.) So in part (a), delete everything from "and" to the end of the sentence. (Thanks to Mohit Gurumukhani, November 2018.)

Page 190

Exercise 13: In part (d), more assumptions are needed: assume that p is not 2, and that p does not divide a. (Thanks to Claus Sorensen, December 2018.)

Page 191

Exercise 17: In part (a), compute "a multiplicative inverse d of e," not "a multiplicative inverse of d." There is also an error in the ciphertext in part (c)! It should be 0802, 2179, 2276, 1024. (Thanks to Erik Wallace, April 2018.)
Chapter 8: Quadratic residues
Page 195
Figure 8.3 Caption: The final congruence should be "mod p." (Thanks to Corey Shanbrom, March 2019.)
Page 195
A French typo, 6 lines from the bottom: "Théoreme" should be "Théorème." (Thanks to Vens Lee, February 2019.)
Page 197
Penultimate sentence: There's a misplaced comma. (Thanks to Corey Shanbrom, March 2019.)

Page 199

In the middle of the page, in the body and in the margin, I've mistakenly described the partnerships between x and -x as "(-1)-partnerships", which is incorrect. I've simply partnered each number x mod p with -x mod p. The rest of the argument (about E and O) is correct. (Thanks to Marco Schockmel, November 2017.)
Page 200
Proof of Proposition 8.8: By a parallelogram "twice as large," I mean that the sides are twice as long. (Thanks to Corey Shanbrom, March 2019.)
Page 200
Overlapping circle figure: It seems like the first-quadrant circle in the left image was shrunk in the second image. (Thanks to the sharp eyes of Pete Morcos, October 2019.)
Page 202
Footnote 9: "was suggested" is repeated twice. (Thanks to Yoc Jer, September 2019.)
Page 204
The caption on Figure 8.9 should say that the red arrow from 2 to 6 displays the data f(2) = 6. (Thanks to Paolo Scarpat, December 2018.)

Page 205

Line 11: h should be g ◦ f , not f ◦ g. (Thanks to Paolo Scarpat, December 2018.)
Page 207
The notation "sgn(f)" refers to the sign of the permutation f. (Thanks to Corey Shanbrom, March 2019.)
Page 212
Sidenote at top: The two equalities should be congruences . (Thanks to Pete Morcos, October 2019.)

Page 213

Second paragraph of the proof of Lemma 8.25: The permutation alpha sends [a,b] to <a,b] (and not the other way around). (Thanks to Marco Schockmel, November 2017.)

Page 215

Solution of Problem 8.28: 42 is not congruent to 1 modulo 7... change that 42 to 43. (Thanks to Firas Melaih, October 2017)
Page 221
Marginnote 34: The 4-sphere should be called the 4-ball. (Thanks to Claus Sorensen, December 2018)

Part III: Quadratic forms

Chapter 9: The topograph

Page 232

Last sentence of 3rd paragraph: there should be plus/minus (\pm) signs, to read "So we prefer \pm (0,1) over \pm (0,-1)."
Page 236
Proof of Thm 9.14, end of 1st paragraph: v and w lost their over-arrows.
Page 249
Top of page, "allow us transform" should be "allow us to transform".
Page 252
Figure 9.29: The terms "definite" and "indefinite" have not yet been defined. Definite forms are those with all-positive or all-negative values. Indefinite forms are those with both positive and negative values. This can be detected by the discriminant, as noted in the figure. (Thanks to Corey Shanbrom, March 2019.)

Page 255

Line 15: 2m + 1 should be 20m + 1. (Thanks to Pete Morcos, October 2019.)
Page 255
Mid-page: "ètre" should be "être." (Thanks to Vens Lee, February 2019.)
Page 255
A clarification: around the quote from Euler (1748), there is a reference to Theorems 10 and 11. This refers to "Theorema 10" and "Theorema 11" from Euler's original work. (Thanks to Pete Gilmore, October 2018)
Page 256
Exercise 7: This exercise should not end in a question mark. (Thanks to Corey Shanbrom, March 2019.)
Chapter 10: Definite forms
Page 270
Marginnote 21: Change "isomorphism" to "isometry."(Thanks to Corey Shanbrom, March 2019.)
Page 271
Figure 10.3 Caption: The final displayed equation should end with a period. Also "primitive classes" should just refer to primitivity of the forms, as in the definition of the class number. (Thanks to Corey Shanbrom, March 2019.)
Page 272
Line 5: zeta(3) is often called Apéry's constant, and is approximately 1.202056903159594. (Thanks to Corey Shanbrom, March 2019.)
Page 277
Marginnote 39, line 4: "l’Acadamie" should be "l’Académie." (Thanks to Vens Lee, February 2019.)
Page 279
Sidenote 29: "Francisc" should be "Francis". (Thanks to Pete Morcos, October 2019.)
Page 279
Exercise 12(c): A period is missing at the end. (Thanks to Corey Shanbrom, March 2019.)
Page 279
Exercise 15: No comma is needed. (Thanks to Corey Shanbrom, March 2019.)
Chapter 11: Indefinite forms
Page 282
Line 8: "a(0)^2" should be "a(1)^2". (Thanks to Pete Morcos, October 2019.)
Page 291
In the two figures, the "v" should be in italics like the other variables.
Page 294
Marginnote 13: This sentence fragment should probably be made into a complete sentence. (Thanks to Corey Shanbrom, March 2019.)
Page 299
Table 11.1: This is an important classification... maybe it should be a theorem, proven earlier. (Thanks to Corey Shanbrom, March 2019.)
Page 300
End of Brahmagupta quote: "Interpolatpors" should be "Interpolators". (Thanks to Pete Morcos, October 2019.)
Page 300
Marginnote 28: A period is missing at the end.(Thanks to Corey Shanbrom, March 2019.)
Page 301
Marginnote 30: A period is missing at the end.(Thanks to Corey Shanbrom, March 2019.)
Page 301
Marginnote 38: Change ArXiv to arXiv. But this article has now been published in Comptes Rendus. (Thanks to Corey Shanbrom, March 2019.)

End matter

Page 315
There should only be one entry for Sunzi (c.220-420CE).
Page 317
Entry for E. Bézout: "a l’usage" should be "à l'usage." Entry for J. Bourgain: "Mathematique" should be "Mathématique." (Thanks to Vens Lee, February 2019.)
Page 318
Entry for Chebyshev: "nouveaux" should be "nouveau" and "mathematique" should be "mathématique" and "l’Academie Imperiale" should be "l’Académie Impériale." (Thanks to Vens Lee, February 2019.)
Page 321
First entry for Lagrange: "théoreme" should be "théorème." (Thanks to Vens Lee, February 2019.)