IR-TST 2009 Problem 11

Let $n$ be a positive integer. Prove that $3^{\dfrac{5^{2^n}-1}{2^{n+2}}} \equiv (-5)^{\dfrac{3^{2^n}-1}{2^{n+2}}} \pmod{2^{n+4}}.$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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