## Description

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.

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