and are two primitive Pythagorean triples

The primitive Pythagorean triples are characterized by

and

for some positive integers and , and that then

For the given Pythagorean triples and ,

where

and

we must have, for some positive integers

**(1)**

or

**(2)**

**(3)**

or

**(4)**

are either a square or twice a square in (1) and (3) , (2) and (4), (1) and (4), (2) and (3)

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Substituting for {a,b,c,x,y,z} the resulting formulae reduces to terms with squares for the latter examples, namely :-

a x + (b y – c z) = 2(n u + m v)^2 and

a x – (b y – c z) = 2(m u – n v)^2

Paul.

It’s either a square or twice a square.

I made a modification