Math 422: Introduction to Number Theory Homework on §7–8
A. Let d | a, d | b. Show that gcd(a, b) = d gcd a d , b d
. B. Silverman 7.3. C. Recall that for n ∈ N, n! means n · (n − 1)· · · 2 · 1. How many 0s does 100! end in? D. Let n ∈ N have prime factorization p e1 1 p e2 2 · · · p er r , where the pi are distinct primes and ei ≥ 1. Show that n is a perfect square if and only if 2 | ei for all i. E. Silverman 8.5–8.7. 1 of 1
