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. 1 of 1
