Each of a, b, c, d and e is a positive integer satisfying this system of equations:

a^{-2} + b^{-2} + c^{-2} = d^{-2}, and:

a+b+c = e^{2}

Determine the smallest value of e. What are the next two smallest values of e?

(In reply to

The value of e by Math Man)

I believe KS was referring to the variable e in the question, not the base of the natural logarithms (aka Euler's constant.) :-)