MathDB

10.4

Part of 2000 Saint Petersburg Mathematical Olympiad

Problems(1)

Prove that a number has at least 19901 divisors

Source: St. Petersburg MO 2000, 10th grade, P4

4/22/2023
The number NN is the product of 200200 distinct positive integers. Prove that it has at least 19901 distinct divisors (including 0 and itself).
[I]Proposed by A. Golovanov
number theoryExistence