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.

Current errata (mathematical errors in red)


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 9
Just above Prop 0.13: "are form a" should be "are from a".
Page 16
The end-of-proof square comes a few lines too early in Proposition 0.27.
Page 21
Exercise 26: "perfect squares" should be called "squares".
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 34
Line 13: "equaions" should be "equation".

Page 36

Proposition 1.20: The integers a,b should both be nonzero.
Page 39
The end-of-proof (QED) square is misplaced. It should be just above Problem 1.24.

**Page 45**

Exercise 14: The last line should read "LCM(u^2, v^2) = LCM(u,v)^2". The final "squared" was forgotten.

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 57
The exponent of 7 should be called f_7, and not f_5, in equations (2.1), (2.2), and (2.3).
Page 68
A period wandered away from 2N, at the bottom of the page.
Page 73
Exercise 18(b): The period should go within the parenthesis at the end.

Chapter 3: Rational and constructible numbers

Page 80

Middle figure: the r^2/d should be r^2/d^2, inside both square roots. As a result, a 1/d could be factored out of the square roots to simplify the expression a bit.
Pages 90-95
I really should have mentioned Farey sequences by name, and in the historical notes.
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): There's an extra period in "cosine.."

Chapter 4: Gaussian and Eisenstein integers

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.
Page 106
Line three: "centered z" should be "centered at z."
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.

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 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 150

Exercise 5: One should assume that m is nonzero. Perhaps even that m is positive, if you don't like negative moduli.

Chapter 6: Modular dynamics

Page 154

In Problem 6.1, there are 7 equal signs that should be congruences instead.
Page 166
In sidenote 7, "precient" should be "prescient". (Thanks to Alberto Trombetta, September 2017.)

Chapter 7: Assembling the modular worlds

Chapter 8: Quadratic residues

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 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)

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".

Chapter 10: Definite forms

Chapter 11: Indefinite forms
Page 291
In the two figures, the "v" should be in italics like the other variables.

End matter


Page 315
There should only be one entry for Sunzi (c.220-420CE).