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Proof by induction

  1. Sep 28, 2011 #1
    Proof by induction that 3 * 5^2n+1) + 2^3n+1 is divisible by 17!
    Thanks in advance guys
     
  2. jcsd
  3. Sep 28, 2011 #2
    In your expression, there is an ")" without an "(" --> 3 * 5^2n+1) + 2^3n+1

    so it is not clear what do to!
     
  4. Sep 28, 2011 #3
    You also need to try yourself and let us know where you're stuck. Then we can help.
     
  5. Sep 28, 2011 #4
    I proved the base case n=1, and then I try doing the step case assuming that it satisfies for any k, then I try proving it by k+1.
    I got sth like 24 * (3 * 5^(2k+1)) + 7 * 2^(3k +1) Now I'm stuck can't continue, I don't have any ideas :/
    btw the initial equation is 3 * 5^(2n+1) + 2^(3n+1) !
     
  6. Sep 28, 2011 #5
    Got it now :) let's denote the initial statement as K + L, so we have sth like 24l + 7k = 7(k+l) + 17k, sum of two numbers divisible by 17 is divisible by 17, anyway thx
     
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