# Kiriti's powers of 2

Algebra Level 3

Let $$a$$ be a positive integer divisible by $$4$$ but not divisible by $$8$$. What is the largest positive integer $$n$$ such that $$2^n$$ divides

$a^{100} + a^{101} + a^{102} + a^{103} + \cdots +a^{1000}?$

This problem is posed by Kiriti M.

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