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Prove this is divisible by 228 for any n

  1. Oct 29, 2012 #1
    1. The problem statement, all variables and given/known data
    Prove that the following is divisible by 228 for any n (natural number).

    [tex]1561^n + 712^n -1225^n - 364^n [/tex]

    2. Relevant equations
    3. The attempt at a solution
    I'm guessing you have to prove by induction. When n = 1, the quotient is 3. What do I do afterwards? Thanks.
     
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  3. Oct 29, 2012 #2

    Simon Bridge

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    Welcome to PF;
    You follow the other steps for induction.
     
  4. Oct 30, 2012 #3

    HallsofIvy

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    In other words, assume that 1561k +712k −1225k −364= 228n for some integers k and n and then show that 1561k+1 +712k+1 −1225k+1 −364 is a multiple of 228.
     
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