Yes. Select any triple and if the first one is not even, then double all three numbers. For example, (3, 4, 5) gives (6, 8, 10).
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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.
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Suppose you are given a number X. Then, if X is odd Y = X2/2 - 1/2 and Z = Y + 1 form a triplet. and if X is even, then Y = X2/4 - 1 and Z = Y + 2 form a triplet.
It is an even number.
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