# Positively hilarious

Let $$b$$ and $$c$$ be positive integers such that the polynomial equations $x^2 + bx + c =0 \text{ and } x^2 + bx - c=0$ both have integer solutions. Determine the sum of all values of $$b \leq 50$$ for which polynomials of this form exist.

Details and assumptions

There is no restriction on the size of $$c$$.

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