Mastering the Euler Phi Function:
a) Compute and
b) Use a counting argument to prove that for p prime and k a positive integer.
Our goal now is to prove the following theorem:
If then 
a) Recalling that and assuming that , prove that the mapping defined by
b) Assuming that the “Baby Chinese Remainder Theorem” stated below is true, prove that is onto.
Let m and n be integers with gcd(m, n) =1, and let b and c be any integers. Then the simultaneous congruences and have exactly one solution with
c) Use parts a) and b) to explain why you now know that implies
Exercise 3. Compute