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Introduction to Number Theory  Homework on 7–8

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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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