Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be...

Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be even and cannot both be odd. Hint: for the odd case, assume that there exists a primitive Pythagorean triple with X and Y both odd. Then use the proposition "A perfect square always leaves a remainder r=0 or r=1 when divided by 4." to produce a contradiction.

Expert Solution

The problem is solved in detail below.

Colby Messinger answered 1 year ago

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Show that if (x,y,z) is a primitive Pythagorean triple, then X and Y cannot both be...

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