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.
