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Save Big on PS Plus Subscriptions—Today’s Pricing is Unbeatable! - Imagemakers

📅 May 1, 2026 👤 scraface

May 01, 2026

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📌 Find the smallest positive integer $n$ such that the fourth power of $n$ ends in 0625.

📌 Thus, the smallest such $n$ is $15$.

📌 Since $m$ and $n$ are coprime positive integers with $m + n = S$, $mn = P$, and $S, P$ related to $d$, we require that the quadratic:

📌 has integer roots. The discriminant must be a perfect square:

📌 Try possible divisors $d$ of 2025, since $d$ divides $a + b = 2025$. Factor $2025$:

📌 Discriminant: $729 - 2640 = -1911 < 0$: no real roots.

📌 Discriminant: $81 - 880 = -799 < 0$: no.

📌 Try $d = 75$: not working. Try $d = 15$:

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