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= -4 + 8 + m - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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:

📌 19y^2 \equiv 0 \pmod{25} \Rightarrow y^2 \equiv 0 \pmod{25} \Rightarrow y \equiv 0 \pmod{5}.

📌 So let $y = 5k$. Substitute:

📌 25x^2 = 144(25k^2) + 3600 = 3600k^2 + 3600 = 3600(k^2 + 1).

📌 Divide both sides by 25:

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