Generally, I am stumped by the Phi function. I have found out the pattern but I am having difficulty proving it.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

i) Whenpis a prime number, obtain an expression in terms ofpfor:-

ϕ(p²)

2. Relevant equations

ϕ(p)=p-1

3. The attempt at a solution

ϕ(p)=p-1

so ϕ(5)=4 thereforep²=5²=25 therefore ϕ(p²)=20

Also, ifp=3 then ϕ(3)=2 therefore ϕ(9)=6

It appears that ϕ(p²)=p(p-1)

My problem is that I am not able to proof it. Yes, the pattern isp(p-1) but I am stuck as to how to explain it. Any soloutions?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Proofing Euler's Phi Function.

**Physics Forums | Science Articles, Homework Help, Discussion**