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Math Help - 3 squares

  1. #1
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    3 squares

    Show that among any 3 consecutive integers, at least one is a sum of three integer squares.

    my working:
    to solve this, lets consider m,m+1,m+2
    we only need to consider the case where m is congruent to 7 mod 8 right?
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  2. #2
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    Crna Gora
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  3. #3
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    Re: 3 squares

    i still do not get it. so if n=4^x(8k+7), we need to show that n+1 or n+2 is not of that form. how do we show that?

    i'm wondering from the link, when we consider n = 8k+7 then n is congruent to 7 mod 8 but if n =4^x(8k+7) then n is congruent to 0 mod 8 if x>3 right? yet why does it say that it cant be a sum of three squares if n = 8k+7 and n =4^x(8k+7)?

    Thank you!
    Last edited by alexandrabel90; April 30th 2012 at 05:09 PM.
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