HOMEWORK ASSIGNMENT 7, DUE IN CLASS THURSDAY, OCTOBER
18, 2007
Reading:
• Read Chapters 6.3, 6.4
Problems to be turned in:
• Chapter 6.8 #19, #27.
• Chapter 6.9 #4, 5, 10, 14.
Additional problems:
(1) Let n = 37241.
(a) Try to factor
with B = 10. Does it work?
√
√ n using Pollard’s p − 1 method,
(b) Let s = b nc be the greatest integer ≤ n. Search through integers of the form
(x + s)2 − n with 1 ≤ x ≤ 40 for integers all of whose prime factors are ≤ 13.
(e.g. 1972 − n = 25 72 , so 1972 ≡ 25 72 (mod n)). List all such congruences.
(c) Using your list of congruences, find x and y such that x2 ≡ y 2 (mod n) but
x 6≡ ±y (mod n). Deduce a factorization of n.
1