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Introduction to Number Theory  Homework on 10–11

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Math 422: Introduction to Number Theory
Homework on 10–11

A. Write a program that takes as input a positive integer n and computes ϕ(n).
You may use brute force.
B. Compute
1. ϕ(81)
2. ϕ(20736)
3. ϕ(10000000000)
C. 1. Find all n for which ϕ(n) = 4.
2. Find all n for which ϕ(n) = 6.
D. Silverman 11.5.
E. Silverman 11.8. You may not use brute force.
F. Silverman 11.9.
G. Show that if gcd(m, n) > 1, then
ψ : Z/mn → Z/m × Z/n
[x] 7→ ([x], [x])
is never bijective.
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