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Help with induction?

  1. Sep 29, 2009 #1
    Question Details:
    show that any number greater than 23 can be written as a sum of 5's and/or 7's


    attempt:
    24: 7 7 5 5
    25: 5 5 5 5 5
    26: 7 7 7 5
    27: 7 5 5 5 5
    28: 7 7 7 7
    29: 7 7 5 5 5
    30: 5 5 5 5 5 5
    31: 7 7 7 5 5
    32: 7 5 5 5 5 5
    33: 7 7 7 7 5
    34: 7 7 5 5 5 5

    from this, i see that this follows a pattern:
    n = f(a,b) = 5a + 7b

    for n> 23


    but how do i go about to prove this for all values?
     
  2. jcsd
  3. Sep 29, 2009 #2
    Could you show that it was true for 24,25,26,27,28 then just say that every number beyond these can be expressed as x + 5n, where x is one of 24,25,26,27,28 and n is a natural number?
     
  4. Sep 30, 2009 #3
    lol yeah. i kinda figured it out similar to that way after taking a long nap. thanks for the response though!
     
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