1. Prove that if p E N is a prime and v E N is such...

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1. Prove that if p E N is a prime and v E N is such that pº | n, then (p-1)p-1 | o(n). Hint: When p is prime, what is (pº)? 2. Using the previous question, prove that if ø(n) = 4, then n cannot be divisible by a prime p≥ 7. Also prove that 3², 5² | n. 3. Find all n such that (n) Hint: Think in terms of the factorisation of n. You should find that there are four such n but you are required to prove this as part of this question! = 4. 1. Prove that if p E N is a prime and v E N is such that pº | n, then (p-1)p-1 | o(n). Hint: When p is prime, what is (pº)? 2. Using the previous question, prove that if ø(n) = 4, then n cannot be divisible by a prime p≥ 7. Also prove that 3², 5² | n. 3. Find all n such that (n) Hint: Think in terms of the factorisation of n. You should find that there are four such n but you are required to prove this as part of this question! = 4.

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Answer 1 We can prove that p1p1 n by using the fact that when p is prime pv p for all v N Since pn t... View the full answer