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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 25x^2 - 144y^2 = 3600.

📌 We seek integer solutions $(x, y)$. Rearranging:

📌 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.

📌 Let $k^2 = \frac{144y^2 + 3600}{25}$. Then:

📌 144y^2 + 3600 \equiv 0 \pmod{25} \Rightarrow 144y^2 \equiv -3600 \pmod{25}.

📌 Since $144 \equiv 19 \pmod{25}$ and $-3600 \equiv 0 \pmod{25}$, we get:

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