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  1. #1
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    Help on proving this statement...

    Prove that if n=2 (mod 3) then it cannot be a square.

    No idea where to start with this one. Any pointers please?
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  2. #2
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    Quote Originally Posted by free_to_fly View Post
    Prove that if n=2 (mod 3) then it cannot be a square.

    No idea where to start with this one. Any pointers please?
    Hmm a table of congruences would work.

    Assume that n=k^2

    \text{If } k=0 \bmod 3 \text{ then } n=k^2=0 \bmod 3

    \text{If } k=1 \bmod 3 \text{ then } n=k^2=1 \bmod 3

    \text{If } k=2 \bmod 3 \text{ then } n=k^2=4 \bmod 3=1 \bmod 3

    And these are all the possibilities. You can see that none of the results are 2 \bmod 3
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  3. #3
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    Quote Originally Posted by free_to_fly View Post
    Prove that if n=2 (mod 3) then it cannot be a square.

    No idea where to start with this one. Any pointers please?
    Here is an interesting fact. The only (odd) primes that have 2 as a square are of the form 8k\pm 1. (Since p=3 does not have this form this form it is not a square of 2. This is not meant to be a proof of what you asked, just an interesting fact).
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