prove to me that the pythagorean triples are from the form 3k,4k,or 5k. for k >=1. proof: cases for 3K: 3k ^2 9k^2 factor out 3k 3k(3k) 3k+1 ^2 9k^2+1 3k(3k)+1 3k+2 ^2 9k^2+1+3 3k(3k)+4 cases for 4k: 4k ^2 16k^2 factor out 4k 4k(4k) 4k+1 ^2 16k^2+1 4k(4k)+1 4k+2 ^2 16k^2+4 4k(4k)+4 4k+3 ^2 16k^2+9 4k(4k)+9 cases for 5k: 5k ^2 you get the idea... 5k+1 5k+2 5k+3 5k+4 would this be the easiest way of doing this type proof? anyone w/ info/suggestions please reply. i know that there are remainders involved, but is there any way of finding out w/o looking at it? i mean, should i ^2 or ^3 them ?