Introduction to Proofs 1.1 Pythagorean Triples. Showing that at least one number is even.

In this video, we are going to use some of the proof techniques to show that at least one number from Pythagorean Triple must be even.

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Please watch: "Real Projective Space, n=1"
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[kinglauip]

If a and b are both odd, then a^2+b^2 must be even. The author has rightly pointed this out in the video.
However, a^2+b^2 cannot be a perfect square as it is not a multiple of 4. Then, the Pythagoras Theorem cannot be applied to a, b and c if a and b are both odd.

So the statement that at least one number of the Pythagorean Triple is even is not precise. It should be changed to "at least one of the legs of the right angle triangle should be even (either a or b should be even)".

The possible parity distributions of the Pythagorean Triple (a, b and c) are:
(even, odd, odd), (odd, even, odd), (even, even, even)
but not (odd, odd, even).

[widscience]

widodo's conjecture (method and equations) to find ALL permutation of pythagorean triples, see the video :

[nabilabushra]

Bekaar ka bakwaa kuch kaam ka ni hai😏😏😠😠😠😠😠