1+1=1
Jul5-04, 10:05 AM
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\equiv0 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.
i need to show that if gcd(a,n)=(a-1,n)=1, then 1+a+a^2...+a^\phi^n^-^1\equiv0 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.