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Thread: Help with Mod Proof

  1. #1
    Junior Member
    Sep 2009

    Help with Mod Proof

    Let n be an odd integer that isn't divisible by 3. Then $\displaystyle n^2 \equiv 1$ mod 24.

    So I have n = 3x+1 and n = 3x+2.

    So 24 | $\displaystyle n^2-1$.

    I'm stuck after this. Should I do the X and get n odd and then do the n^2 or?....

    EDIT: I figured out that if I can get n^2 - 1 mod 3 and n^2 - 1 mod 8 then X is a divisor of n^2-1 where X is the least common multiple of 3 and 8. So then that would be 24. So I just need the mod 3 and mod 8 but I can't get them quite right.
    Last edited by JSB1917; Feb 20th 2011 at 03:19 PM.
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  2. #2
    Senior Member
    Nov 2010
    Staten Island, NY
    Here's a hint to get you started. An odd integer has the form 2k+1 for some integer k.
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