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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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Advance Math

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

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