MathDB

For each positive integer

n

, let

rad(n)

denote the product of the distinct prime factors of

n

. Show that there exists integers

a,b > 1

such that

gcd(a,b)=1

and

rad(ab(a+b)) < \frac{a+b}{2024^{2024}}

.
For example,

rad(20)=rad(2^2\cdot 5)=2\cdot 5=10

Problem Statement