Q13/005) If an integer sided right triangle has two prime sides, must the difference of some two sides equal one?

If x y z are a triple then

x^2+y^2 = z^2

=> x^2 = (z^2-y^2)= (z+y)(z-y)

if x is prime then x^2 cannot have 2 different factors

(z-y) and (z+y) being different so z –y has to be 1