Easy Proof Help

Quote:

Originally Posted by Jimbobobo

PROVE THE FOLLOWING:
a^2 + b^2 = c^2 then; a or b can be divided by 3.

1. Every square is congruent to 1 or 0 modulo 3, left to the reader to prove.

2. If neither a^2 nor b^2 is congrent to 0 modulo 3, then c^2 is congruent
to 2 modulo 3 which is not possible, hence at least one of a^2 or b^2 is
congrent to 0 modulo 3.

3. If x^2 is congruent to 0 modulo 3 then so is x, hence either a or b must
be congrent to 0 modulo 3.

RonL