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Thread: Proof by contradiction. Show that there is no positive integer x and y such that x^2

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    Proof by contradiction. Show that there is no positive integer x and y such that x^2

    Show that there is no positive integer x and y such that x^2 - y^2=1

    Pls show detailed working.
    Last edited by cocoboy; Oct 16th 2017 at 10:09 AM.
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    Re: Proof by contradiction. Show that there is no positive integer x and y such that

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    Re: Proof by contradiction. Show that there is no positive integer x and y such that

    Quote Originally Posted by cocoboy View Post
    Show that there is no positive integer x and y such that x^2 - y^2=1
    Suppose that each of $m~\&~n$ is an integer and $m>n$. You must answer the questions and post the answers.

    a) Suppose $m^2-n^2=1$ How does that tell us that $m>n~\&~n\ne 1?$ (you must post answers)

    b) The fact that $n\ne 1$ means that $n\ge 2$ Explain why.

    c) $ \begin{align*}m+n&>2n ~\text{WHY}?? \\2n&\ge 4~\text{WHY}??\\(m+n)(m-n) &\ge 4(m-n)~\text{WHY}??\\1 &\ge 4(m-n)\text{WHY}?? \end{align*}$

    Where is the contradiction and what is contradicted?
    Thanks from topsquark
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