Does exponent matter?

Algebra Level pending

Let ( x i , y i ) (x_i, y_i) be ordered pair of solutions of the equation x y + y x = x + y x^y + y^x = x + y such that x i ≤ y i ; x i , y i ∈ Z ; x i , y i ∈ [ 0 , 1000 ] x_i \leq y_i; x_i, y_i \in \mathbb{Z}; x_i, y_i \in [0, 1000] Evaluate ∑ x i + y i \sum_{}^{} x_i + y_i


The answer is 501501.

Jimmy PrevailLone by Jimmy PrevailLone , 23, Thailand

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