For integer m greather than 2, $\frac{1}{m} + \frac{1}{m+2}$, the numerators and denomitors are primitive pythagorean triples $a$ and $b$ For $m = 2$, the fraction is $\frac{3}{4}$. for $m=3$, the fraction is$\frac{8}{15}$. I was wondering why numerators and demoninators of  $\frac{1}{m} + \frac{1}{m+2}$ show primitive pythagorean triples a and b.

There is a simple form to proof:
$(m^2+2m)^2 + (2(m+1))^2 = ((m+1)^2 - 1)^2 + 4 (m+1)^2 = (m+1)^4 + 1 -2(m+1)^2 + 4(m+1)^2 = (m+1)^4 -2(m+1)^2 + 1 = ((m+1)^2 - 1)^2$
