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Math Help - Prove that the equation x^2 equivalent tio 2 mod 3 has no solution with x in Z.

  1. #1
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    Prove that the equation x^2 equivalent tio 2 mod 3 has no solution with x in Z.

    Hi, I have the following problem. I think I know how to solve the second part (I have done 2 other problems that look very similar), however, I have no clue about the first part :-/. Thanks for your help!

    Part 1 (the one I have no clue about): Prove that the equation x^2 \equiv 2 mod 3 has no solution with x in \mathbb{Z}.
    Part 2 (which I think I know): Then use this to prove that the equation x^2 = 2+3y has no solution with x and y in \mathbb{Z}
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  2. #2
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    Hint: Consider all possible remainders when x is divided by 3.
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