# Modulos raised to phi

1. Jul 5, 2004

### 1+1=1

hi, it's me again, i only have 3 tiny questions then i am done asking, i hope!

i need to show that if gcd(a,n)=(a-1,n)=1, then 1+a+$$a^2$$...+a^$$\phi^n^-^1\equiv$$0 mod n

show (m,n)=1 then m$$^\phi^n+n^\phi^m\equiv$$ 1 mod (mn)

show if m and k are positive integers then $$\phi$$(^k)=m^k-1$$\phi$$(m)

what i know so far: the second one can use fermat's little theroem correct? if a==0 mod b and b==0 mod a then => ab==0 mod(ab)

the third one is just playing with my brain, i honestly do not know anywhere to start it.

the first question says what a,n are relatively prime, and a-1,n are also relatively prime. so, if any a raised to a power, that a is == to 0, mod n. can anyone give me a "hint"?

thank you!! p.s. does my LaTeX look good? feel free to tell me and all.

Last edited: Jul 5, 2004
2. Jul 5, 2004

### 1+1=1

can anyone help me with these? i honestly have no idea how to start any of them... i just need a little "boost"