This is a short and rather incomplete list of errata for Melvyn B. Nathanson’s **Elementary Methods in Number Theory**, Springer, Graduate Texts in Mathematics, **vol. 195**, (2000), MR1732941 (2001j:11001), compiled while teaching Math 507 – Advanced Number Theory in Fall 2010.

**Chapter 1**

Page 7. Exercise 8. that that if

Page 8. Exercise 9. that that if

Page 9. Exercise 25.(a). *reflexive* in *reflexive* (or *anti-symmetric*) in

Page 10. Line break needed in line 4.

Page 12. Line -11. every nonempty every such nonempty

Page 12. Line -8. integers has integers, not all 0, has

Page 14. Line -9. integers integers, not all 0

Page 20. Line break needed in line -11.

Page 31. Line 11.

Page 36. Line 1. integers integers with

Page 37. Line 12. 14 13

Page 40. Line 12.

Page 41. Line break needed in line 8.

Page 43. The last paragraph can be updated as follows: By September, 2010, a few more Mersenne primes have been found. The list continues with for 13,466,917; 20,996,011; 24,036,583; 25,964,951; 30,402,457; 32,582,657; 37,156,667; 42,643,801; and 43,112,609. It is not known whether this list includes all Mersenne primes less than or equal to , or if some have been skipped. The largest known prime is .

**Update, January 4, 2018:** The largest known prime is now for , a number with digits. It was identified on December 26, 2017. See here for the announcement and further details.

**Chapter 2**

Page 48. Line 6.

Page 53. Line 14. to for

Page 57. Line 17.

Page 57. Line 18.

Page 58. Line breaks needed in lines -7 and -4.

Page 61. Exercise 11.

Page 68. Line -15.

Page 72. Exercise 6. into into

Page 78. Line 7. If . If

**Chapter 3**

Page 90. Line break needed in line 1.

Page 91. Line 5. , not both 0

Page 95. Line 10. of theorem of the theorem

Page 98. Line 5.

Page 98. Line 14. 5, 4 5

Page 99. Line -4.

Page 108. Line -2.

Page 108. Line -1.

Page 109. Line break needed in line 13.

Page 114. Exercise 5. quaratic quadratic

Page 114. Exercise 6. quaratic quadratic

Page 118. Line -13.

**Chapter 4**

Page 122. Line 8.

Page 124. Line 2.

Page 124. Line 12.

Page 125. Exercise 8(b).

Page 125. Line break needed in line -2.

Page 126. Line -6.

Page 127. Line 2.

Page 128. Line -2. for all for all

Page 134. Line 11.

Page 134. Line 12. defined is defined

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Page 138. Line 5. (Twice)

Page 138. Line 5.

Page 138. Lines 7, 8.

Page 138. Line -8.

Page 140. Line 6.

Page 140. Line 6.

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Page 142. Line 9. is evaluated at is

Page 142. Line -6. It Since is an isomorphism, it

Page 143. Exercise 3. G/H

Page 145. Line 5.

Page 146. Line -15.

Page 147. Theorem 4.14.* group* *group of order *

Page 149. Theorem 4.15. *For* *Let be a finite abelian group of order . For*

Page 149. Line -2. then then (with )

Page 150. Line -7.

Page 151. Line 2.

Page 154. Theorem 4.18.* is prime* *is an odd prime*

Page 155. Lines 3 (twice), 4, 5, 6, 8, 11.

Page 157. Line 9. 10 13

Page 157. Line -8.

Page 157. Line -6.

Page 157. Lines -5, -3.

Page 160. Line -10. a a a

Page 162. Line break needed in line -5.

Page 163. Line break needed in line 2.

Page 163. Line 12.

Page 169. Line 5. appears appears in

**Chapter 5**

Page 174. Line -8.

**Chapter 6**

Page 220. Remove line 4.

**Chapter 8**

Page 271. Line 3.

This is a great post. Thank you.

Luca Goldoni Ph.D University of Trento Italy

A new update: https://www.mersenne.org/primes/?press=M82589933 The current record for largest known prime is for .