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Math Help - Stumped, please help

  1. #1
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    Stumped, please help

    prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
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  2. #2
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    Quote Originally Posted by bearej50 View Post
    prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
    Think about the ways that you can express n as an even integer and as an odd integer. To start, for y = 0, n = 2x accounts for all even integers...
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  3. #3
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    Prove by induction.

    Base Case is fairly easy.

    The inductive step is done in two parts.
    i) When x>0 (replace x by x-1 and y by y+1 and you have n+1)
    ii) When x=0 (replace y by y-1 and x by x+2 and you have n+1)
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  4. #4
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    Quote Originally Posted by bearej50 View Post
    prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
    If n is even then we can write n = 2x. If n>2 is odd then n-3 is even and then n-3=2x\implies n = 2x + 3.
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