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Pythagorean triplets
Fermat's triplets * * * * * No, wrong mathematician. They are Pythagorean triplets.
Pythagorean triplets.
How about 3, 4 and 5 or 6, 8 and 10 in fact any of a Pythagorean triplets will are possible.
Yes. The square of an odd number is odd. So, if a, b and c are odd then a2, b2 and c2 are also all odd. But the sum of two odd numbers must be even. So for these to be Pythagorean, all three squares cannot be odd. Thus there are no odd triplets.