<s>[INST] How to compute the Pythagorean triple by one of the numbers that belonged to it? I have a positive number $n>2$. How to compute the Pythagorean triple containing $n$? $n$ may be the hypotenuse and leg.
 [/INST] If $a$ is the smallest leg then you can find others in very simple way-
If $a$ is odd then -
$$b = \dfrac{n^2-1}{2};\; c = \dfrac{n^2+1}{2}\\ 
[\dfrac{n^2-1}{2}]^2 + n^2 = [\dfrac{n^2+1}{2}]^2$$
If $a$ is even then -
$$b = \dfrac{n^2}{4}-1;\; c = \dfrac{n^2}{4}+1\\ 
[\dfrac{n^2}{4}-1]^2 + n^2 = [\dfrac{n^2}{4}+1]^2$$   
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