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 Toolkit 30 — Vieta's Formula.
From Vieta's Formula,
From Vieta's Formula,
Therefore,
The number of positive integer divisors ofis
441