Hey all, I've got a few problems that are tripping me up tonight. 1. Let m,n be positive integers with m|n. Prove phi(mn)=m*phi(n). I know I can write n as a multiple of m, and m as a product of primes, and my best guess so far is that I can work with some basic properties of or formulas for the phi function to get the desired result. But I'm not making much progress. 2. Let n be an integer with 9|n. Prove n^7 = n mod 63. In this case I know it is enough to prove 7|(n^7-n) and 9|(n^7-n). But even though I imagine this would be a pretty simple application of Euler's theorem, I can't figure it out so far. 3. Suppose p is prime and p = 3 mod 4. Prove ((p-1)/2)! = +/- 1 mod p. This one has me stumpted totally.