AIME I 2026 (Problem 6)
The product of all positive real numbers satisfying the equationis an integer . Find the number of positive integer divisors of .
LetThen
impliesTherefore,so
and therefore
Rearrange the equation asThe product of all positive real solutions is
Use Vieta's Formula.
From Vieta's Formula,
From Vieta's Formula,
Therefore,
The number of positive integer divisors ofis
441