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:

- Your full name, especially if you would like acknowledgment in future editions and on this errata page.
- The page and location (e.g., line 10, beginning of the Proof, etc.) of the mistake.
- A brief description of the mistake, and how you might fix it (optional).
- Any other relevant information, e.g., how many students worked all night on an impossible exercise because of my error.

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.

- 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.)

- 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.

- 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.

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.."

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.

- 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.

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.)

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)

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 291
- In the two figures, the "v" should be in italics like the other variables.

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