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Modulos raised to phi

  1. Jul 5, 2004 #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+[tex]a^2[/tex]...+a^[tex]\phi^n^-^1\equiv[/tex]0 mod n

    show (m,n)=1 then m[tex]^\phi^n+n^\phi^m\equiv[/tex] 1 mod (mn)

    show if m and k are positive integers then [tex]\phi[/tex](^k)=m^k-1[tex]\phi[/tex](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. jcsd
  3. Jul 5, 2004 #2
    can anyone help me with these? i honestly have no idea how to start any of them... i just need a little "boost"
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