Suppose $a$ is a positive integer. When do the totient values of $a$ , $a+1$ and $a+2$ form a pythagorean triple ? In other words :
For which positive integers $a$ does the equation $$\phi(a)^2+\phi(a+1)^2=\phi(a+2)^2$$ hold ?
I yet only found the tripel $[80,60,100]$ appearing for $a=123$. Is it the only one ?