AIME II 2025 (Problem 4)

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The product

\displaystyle \prod_{k=4}^{63}\frac{\log_k(5^{k^2-1})}{\log_{k+1}(5^{k^2-4})}

is equal to

\frac{m}{n}

, where

m

and

n

are relatively prime positive integers. Find

m+n