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25x^2 = 144y^2 + 3600.
We analyze modulo small values. First, note that $x^2 \geq 144$, so $|x| \geq 12$. Try small integer values of $y$ and check if $25x^2 = 144y^2 + 3600$ yields a perfect square for $x^2$.
Let’s suppose $y$ is such that $144y^2 + 3600$ is divisible by 25 and results in a square.

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