Prove that ifthen 60|xyz (where x, y and z are positive integers).
Pythagorean triples are of the form
whereare positive integers with .
So we want to show that
is divisible by 30, i.e. by 2, 3 and 5.
N is even if one of a and b is even. If theyre both odd, then their sum is even, so N is again even.
If neither a nor b is divisible by 3, then one of the following happens:
In cases (i) and (ii),; in case (iii), .
Then by Fermats little theorem,; .
Last edited by JaneFairfax (2008-11-27 14:56:23)