Calculate : $(8^{2^{6^{4^{2^{5^{8^9}}}}}}) (\mod 10000)$ But, the problem is that $8$ and $10000$ are not co-prime. Moreover, the goal is to use Euler's theorem (modified?) to solve this. Any help is appreciated.
2026-03-25 21:53:27.1774475607
Solving modular exponentiation
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HINT: since they are not coprime, what can you say about the powers of $2$ involved here? And then work with the powers of $5$ and combine results (this is related to the Chinese Remainder Theorem, but you don't need to know that actually to solve the problem).