Find (with proof) all Pythagorean triples (not necessarily primitive) with all t

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The formula for generating primitive Pythagorean primes is (http://en.wikipedia.org/wiki/Pythagorean_triple ) x=m^2-n^2, y=2mn, z=m^2+n^2, with m>n, positive integers m,n coprime and m-n odd. Example: 1) n=1, so m is even n=1, m=2 , x=3, y=4, z=5 (and multiples of these, since they are primitive. So we get (6,8,10),(9,12,15),(12,16,20),(15,20,25),(18,24,30),(21,28,35),(24,32,40)) n=1, m=4, x=15, y=8, z=17 (and multiple (8,30,34)) n=1, m=6, x=35, y=12, z=37 we stop here because m^2 will pass 40 2) n=2, so m is odd n=2, m=3, x=5, y=12, z=13 (and multiples (10,24,26),(15,36,39)) n=2, m=5, x=21, y=20, x=29 3) n=3, m=4, x=7, y=24, z=25

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