2025 SSMO Team Round Problems/Problem 7

Problem

Let $n$ be the largest integer such that $20!^{25!} + 25!^{20!}$ is divisible by $2025^n$ . The value of $n$ can be written in the form $a\cdot b!,$ where $a$ and $b$ are positive integers and $b$ is maximized. Find $a+b$ .

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2025 SSMO Team Round Problems/Problem 7

Problem

Solution