# 2016-21 Bound on the number of divisors

For a positive integer $$n$$, let $$d(n)$$ be the number of positive divisors of $$n$$. Prove that, for any positive integer $$M$$, there exists a constant $$C>0$$ such that $$d(n) \geq C ( \log n )^M$$ for infinitely many $$n$$.

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