Problem #PRU-5024

Problem

The real numbers $a, b, c$ are non-zero and satisfy the following equations: ${\begin{cases} a^{2} + a = b^{2} \\ b^{2} + b = c^{2} \\ c^{2} + c = a^{2} . \end{cases}$ Show that $(a - b) (b - c) (c - a) = 1$ .

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