MathDB

Bound of prime factors implying product of many factors

Source: Tuymaada 2021/J6

July 30, 2021

number theory

Problem Statement

Given are real

y>1

and positive integer

n \leq y^{50}

such that all prime divisors of

n

do not exceed

y

. Prove that

n

is a product of

99

positive integer factors (not necessarily primes) not exceeding

y