A Modular Exponential Sequence

A sequence \(a_1, a_2, a_3, ...\) is defined as

\(a_n = 2^n \pmod {100}\).

It starts off as \(2, 4, 8, 16, ...\). Find the last term before the sequence repeats.


This problem is based off Finn Hulse's problem, A Modular Recursion Sequence.

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