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System of equations has no integer solutions

Source: Poland Math Olympiad 1993 Round 1 #1

June 3, 2023
algebrasystem of equations

Problem Statement

Prove that the system of equations { a2−b=c2 b2−a=d2 \begin{cases} \ a^2 - b = c^2 \\ \ b^2 - a = d^2 \\ \end{cases} has no integer solutions a,b,c,da, b, c, d.
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