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Math Help - Does this equation have an integer solution?

  1. #1
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    Red face Does this equation have an integer solution?

    Hi everyone!

    I have the following problem:

    Which of these equations have an integer solution:

    3731s + 6149t = 26

    1001s + 2261t = 1

    495s + 1704t = 1

    385s + 17081t = 1

    I thought the first one would not have an integer solution because 26 is not the gcd of 3731 and 6149, but 13 is. So I thought that it does not have an integer solution because if it did the equation would have to be 3731s + 6149t = 13, but according to the answer key it does have an integer solution. Could anyone explain why?

    Thank you everyone!
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  2. #2
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    Re: Does this equation have an integer solution?

    If 3731s + 6149t = 13 then 3731(2s) + 6149(2t) =26.
    Thanks from Nora314
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  3. #3
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    Re: Does this equation have an integer solution?

    Ah of course thank you so much!
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