Number Theory Proof Help: Show p-1 & p^(e-1)|∅(n)

[rechinball]

hey guys been staring at this question for a few days and frustratingly nothing springs to mind. If any1 could offer some direction that would be awsome :)

let n be a positive integer, and let p be a prime. Show that if e is a positive integer and p^e|n then p-1|∅(n) and p^(e-1)|∅(n)

 

[mathwonk]

explain your notation and you will likely get more answers.

 

[Deveno]

my guess is he(?) intends to indicate the totient function.

 

[20Tauri]

I'm assuming you're using ∅ to indicate Euler's Totient Function/the Euler Phi-Function.

The definition of the totient function/Euler Phi-Function I learned for a natural number n with prime factorization p1^a1 *p2^a2***pn^an, where some of the exponents may be 0 is:

(p1-1)*p1^(a1-1)*(p2-1)*p2^(a2-1)***(pn-1)*pn^(an-1).

So if you know that p^e divides n, the rest should follow from the definition of the Euler Phi-Function.