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Thread: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

  1. #1
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    Exclamation Show there exist integers j and k such that aj + a^2b^2 + bk = 1

    Question: Let a and b be relatively prime positive integers. Show there exist integers j and k such that aj + a^2b^2 + bk = 1.

    I believe I have to do something like letting j and k be elements of a set of something, but I could very easily be mistaken.
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    Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

    Hey azollner95.

    The j and k are indices and the sets contain the pair of numbers where the two numbers are relatively prime.

    So you have a set of pairs (ai,bj) where (ai,bj) are relatively prime.
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    Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

    Hi chiro! When you wrote (ai,bj), did you mean 'ak', and not 'ai'?
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    Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

    No intention to bump, but could anyone clarify on what they could have possibly meant, or if their calculations were correct/accurate.
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    Re: Show there exist integers j and k such that aj + a^2b^2 + bk = 1

    They are just indices so interpret them as that - you can make them whatever letters you like.
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