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Math Help - Help with a modular arithmetic proof

  1. #1
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    Help with a modular arithmetic proof

    Show that there is no solution of "x2 is congruent to 3 modulo 5".
    This is part of a piece of coursework I have for my Mathematical Foundations module but the lecturer barely covered modular arithmetic and i'm pretty terrible at proofs, so any help would be greatly appreciated, thanks.
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  2. #2
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    Re: Help with a modular arithmetic proof

    Every integer x equals 0, 1, 2, 3 or 4 modulo 5, and if x\equiv k\pmod{5}, then x^2\equiv k^2\pmod{5}. So you only need to check that k^2\not\equiv3\pmod{5} for k = 0, 1, 2, 3, 4,
    Thanks from dom139
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