Find all positive integer solutions to the equation $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c^2}$ Find all positive integers to the equation $\frac{1}{a^2}+\frac{1}{b^2}=\frac{1}{c^2}$ 
Multiply both sides with $(abc)^2$ to get $(bc)^2 + (ac)^2 = (ab)^2$.
I then tried some pythagorean triples and nothing worked so I assumed that there arent any solutions. Thank you for your responses.

As you noted $1/a^2+1/b^2=1/c^2 \iff b^2+a^2=\frac{b^2a^2}{c^2}$.
This implies that $a$ and $b$ are part of a pythagorean triple and can hence be written $a=k(m^2-n^2)$ and $b=2kmn$.
We therefore have $a^2+b^2=k^2(m^4-2m^2n^2-n^4+4m^2n^2)=k^2(m^2+n^2)^2$
So we need for $k^2(m^2+n^2)^2$ to divide $2k^4(m^2-n^2)m^2n^2$.
The number of solutions is clearly infinite, for every $m$ and $n$ we have an infinite number of solutions, we just need to take $k$ so that $(m^2+n^2)^2| 2k^2(m^2-n^2)m^2n^2$.
