Number Theory – Errata

This is a list in progress of Errata for Melvyn B. Nathanson, Elementary Methods in Number Theory, Springer, Graduate Texts in Mathematics, vol. 195, (2000). I will be adding to the list as I find time; please let me know of additional typos/corrections you may find.

Chapter 1

Page 7. Exercise 8. that n Longrightarrow that if n

Page 8. Exercise 9. that n Longrightarrow that if n

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

Page 10. Line break needed in line 4.

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

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

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

Page 20. Line break needed in line -11.

Page 31. Line 11. mp_i^{-k_i} Longrightarrow mp_i^{-r_i}

Page 36. Line 1. integers Longrightarrow integers with n>1

Page 37. Line 12. 14 Longrightarrow 13

Page 40. Line 12. x_1 Longrightarrow x_2

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 M_n=2^n-1 for n=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 m=43,112,609. It is not known whether this list includes all Mersenne primes less than or equal to M_m, or if some have been skipped. The largest known prime is M_m.

Chapter 2

Page 48. Line 6. m{mathbf Z}) Longrightarrow m{mathbf Z}

Page 53. Line 14. to Longrightarrow for

Page 57. Line 17. varphi(2)=2 Longrightarrow varphi(2)=1

Page 57. Line 18. varphi(3)=3 Longrightarrow varphi(3)=2

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

Page 61. Exercise 11. varphi(p^k)=varphi(p) Longrightarrow f(p^k)=f(p)

Page 68. Line -15. p Longrightarrow m

Page 72. Exercise 6. 7 into 1 Longrightarrow 1 into 7

Page 78. Line 7. m If Longrightarrow m. If

Chapter 3

Page 90. Line break needed in line 1.

Page 91. Line 5. F[x] Longrightarrow F[x], not both 0

Page 95. Line 10. of theorem Longrightarrow of the theorem

Page 98. Line 5. displaystyle frac{r_n}{3^n} Longrightarrow displaystyle frac{r_n}{2^n}

Page 98. Line 14. 5, 4 Longrightarrow 5

Page 99. Line -4. pmod3 Longrightarrow pmod {19}

Page 108. Line -2. left(frac{q}{u_1!dots u_k!}right) Longrightarrow binom{q}{u_1,dots,u_k}=frac{q!}{u_1!dots u_k!}

Page 108. Line -1. displaystyle left(frac{q}{u_1!dots u_k!}right) Longrightarrow displaystyle binom{q}{u_1,dots,u_k}

Page 109. Line break needed in line 13.

Page 114. Exercise 5. quaratic Longrightarrow quadratic

Page 114. Exercise 6. quaratic Longrightarrow quadratic

Page 118. Line -13. t Longrightarrow x

Chapter 4

Page 122. Line 8. G(p) Longrightarrow G(p_i)

Page 124. Line 2. opluscdotsoplus Longrightarrow +cdots +

Page 124. Line 12. G_1oplus+cdots+oplus G_k Longrightarrow G_1opluscdotsoplus G_k

Page 125. Exercise 8(b). cdots r_k Longrightarrow cdots=r_k

Page 125. Line break needed in line -2.

Page 126. Line -6. =chi(g)chi^{-1}(g) Longrightarrow chi(g)chi^{-1}(g)

Page 127. Line 2. chi(g)barchi)(g) Longrightarrow chi(g)barchi(g)

Page 128. Line -2. chi_i(g_1)=1 for all g_iin G_i Longrightarrow chi_i(h)=1 for all hin G_i

Page 134. Line 11. displaystyle sum xin G f(x) Longrightarrow displaystyle sum_{xin G}f(x)

Page 134. Line 12. L^2(G) defined Longrightarrow L^2(G) is defined

Page 137. Line -1. displaystyle sum_{chiintext{normalsize supp}(hat f)} Longrightarrow displaystyle sum_{chiintext{supp}(hat f)}

Page 138. Line 2. displaystyle sum_{chiintext{normalsize supp}(hat f)} Longrightarrow displaystyle sum_{chiintext{supp}(hat f)}

Page 138. Line 5. (Twice) displaystyle sum_{chiintext{normalsize supp}(hat f)} Longrightarrow displaystyle sum_{chiintext{supp}(hat f)}

Page 138. Line 5. = Longrightarrow le

Page 138. Lines 7, 8. displaystyle sum_{chiintext{normalsize supp}(hat f)} Longrightarrow displaystyle sum_{chiintext{supp}(hat f)}

Page 138. Line -8. supp Longrightarrow text{supp}

Page 140. Line 6. underbrace{chi*cdots*chi}_{displaystyle k text{normalsize  times}} Longrightarrow underbrace{chi*cdots*chi}_{k text{ times}}

Page 140. Line 6. x_k) Longrightarrow x_k)=chi(a)|G|^{k-1}

Page 140. Line 10. underbrace{ell_p*cdots*ell_p}_{displaystyle k text{normalsize  times}} Longrightarrow underbrace{ell_p*cdots*ell_p}_{k text{ times}}

Page 142. Line 9. f^sharp is Longrightarrow f^sharp evaluated at chi^sharp is

Page 142. Line -6. It Longrightarrow Since pi^sharp is an isomorphism, it

Page 143. Exercise 3. G/H Longrightarrow G/H

Page 145. Line 5. {mathcal B} Longrightarrow {mathcal B}'

Page 146. Line -15. {mathcal B} Longrightarrow {mathcal B}'

Page 147. Theorem 4.14. group Longrightarrow group of order n

Page 149. Theorem 4.15. For Longrightarrow Let G be a finite abelian group of order n. For

Page 149. Line -2. then Longrightarrow then (with n=|G|)

Page 150. Line -7. C_{y^sharp} Longrightarrow C_{f^sharp}

Page 151. Line 2. barchi(x),= Longrightarrow barchi(x)=

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

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

Page 157. Line 9. 10 Longrightarrow 13

Page 157. Line -8. underbrace{hat{ell_p}*cdots*hat{ell_p}}_{displaystyle k text{normalsize  times}}=widehat{underbrace{ell_p*cdots*ell_p}_{displaystyle k text{normalsize  times}}} Longrightarrow underbrace{hat{ell_p}timescdotstimeshat{ell_p}}_{k text{ times}}=widehat{underbrace{ell_p*cdots*ell_p}_{k text{ times}}}

Page 157. Line -6. widehat{widehat{underbrace{ell_p*cdots*ell_p}_{displaystyle k text{normalsize  times}}}} Longrightarrow widehat{widehat{underbrace{ell_p*cdots*ell_p}_{k text{ times}}}}

Page 157. Lines -5, -3. underbrace{ell_p*cdots*ell_p}_{displaystyle k text{normalsize times}} Longrightarrow underbrace{ell_p*cdots*ell_p}_{k text{ times}}

Page 160. Line -10. a a Longrightarrow a

Page 162. Line break needed in line -5.

Page 163. Line break needed in line 2.

Page 163. Line 12. frac{(k-j)pi}{n}) Longrightarrow frac{(k-j)pi}{n}

Page 169. Line 5. appears Longrightarrow appears in

Chapter 5

Page 174. Line -8. displaystylebigcap_{Iin{displaystyletext{Spec}}(R)} Longrightarrow displaystyle bigcap_{Iintext{Spec}(R)}

Chapter 6

Page 220. Remove line 4.

Chapter 8

Page 271. Line 3. B Longrightarrow Bx

One Response to Number Theory – Errata

  1. Luca Goldoni says:

    This is a great post. Thank you.

    Luca Goldoni Ph.D University of Trento Italy

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: