# Help with a modular arithmetic proof

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• December 11th 2012, 06:32 AM
dom139
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.
• December 11th 2012, 06:38 AM
emakarov
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,
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