IMO 2024 Shortlist N5
Let S be a finite nonempty set of prime numbers. Let 1 “ b1 ă b2 ă ¨¨¨ be the sequence of all positive integers whose pr...
Category: Number Theory
Problem
Let S be a finite nonempty set of prime numbers. Let 1 “ b1 ă b2 ă ¨¨¨ be the
sequence of all positive integers whose prime divisors all belong to S. Prove that, for all but
finitely many positive integers n, there exist positive integers a1, a2, ..., an such that
a1
b1
a2 b2 ¨¨¨ an bn “ R b1
b2
¨¨¨
bn
V
.
(Croatia)