ILL 1979 Problem 69

Let $N$ be the number of integral solutions of the equation $x^2 - y^2 = z^3 - t^3$

satisfying the condition $0 \leq x, y, z, t \leq 10^6$ , and let $M$ be the number of integral solutions of the equation $x^2 - y^2 = z^3 - t^3 + 1$

satisfying the condition $0 \leq x, y, z, t \leq 10^6$ . Prove that $N >M.$

Dataset text AoPS wiki problems. Quoted with source.

Solutions

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