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Proof help

  1. Aug 5, 2009 #1
    Hello,
    how to prove
    If 7|(a^2+b^2) then 7|a and 7|b.
    (If seven divides a^2+b^2 then seven divides a and seven divides b)
    Thanks.
     
  2. jcsd
  3. Aug 5, 2009 #2

    tiny-tim

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    Homework Helper

    Hello lukaszh! :smile:

    (try using the X2 tag just above the Reply box :wink:)
    Hint: what are 12, 22, 32 etc (mod 7)? :wink:
     
  4. Aug 5, 2009 #3
    12=1 (mod7)
    22=4 (mod7)
    32=2 (mod7)
    42=2 (mod7)
    52=4 (mod7)
    62=1 (mod7)
    72=0 (mod7)
    Is it periodic {1,4,2,2,4,1,0} ? Now I know :-) It's periodic, so if I add any of these congruences together there will be some remainder. Remainder is zero if and only if I add congruences in form
    (7k)2=0 (mod7)
    (7j)2=0 (mod7)
    THANX :-)
     
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