AIME II 2026 (Problem 9)
Let denote the value of the infinite sum Find the remainder when the greatest integer less than or equal to is divided by .
Similarly,
Using Hints 1–3,
where is the number of positive divisors of .
where is the number of positive divisors of .
Multiply both sides by .
Let
Prove that
Prove that
Let
Then
Since
we get
Then
Since
we get
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