Hey all, I've got a few problems that are tripping me up tonight.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Number theory questions

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