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Math Help - Eqaution with 2 variables

  1. #1
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    Eqaution with 2 variables

    Prove that there do not exist integers m,n \in \mathbb{Z} such that 14m + 20n = 119

    Im not quite sure how to go about proving this
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  2. #2
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    Quote Originally Posted by Stylis10 View Post
    Prove that there do not exist integers m,n \in \mathbb{Z} such that 14m + 20n = 119

    Im not quite sure how to go about proving this
    Notice that the two coefficients, 14 and 20, are both even. That is, they are divisible by 2 and, no matter what m and n are, 14m+ 20n= 2(7m+10n) is divisible by 2.
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  3. #3
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    Quote Originally Posted by HallsofIvy View Post
    Notice that the two coefficients, 14 and 20, are both even. That is, they are divisible by 2 and, no matter what m and n are, 14m+ 20n= 2(7m+10n) is divisible by 2.
    I realised that, but surely that cant be the whole proof, i just dont know how to give more that what you have said, that answer alone cant be worth 4 marks
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