prove to me that the pythagorean triples are from the form 3k,4k,or 5k. for k >=1.(adsbygoogle = window.adsbygoogle || []).push({});

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 ?

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# Prove to me that the pythagorean triples

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