MathDB

product of all elements in S is the square of an integer

Source: Vietnam TST 2002 for the 43th IMO, problem 3

June 26, 2005

number theory unsolvednumber theory

Problem Statement

Let

m

be a given positive integer which has a prime divisor greater than

\sqrt {2m} +1

. Find the minimal positive integer

n

such that there exists a finite set

S

of distinct positive integers satisfying the following two conditions: I.

m\leq x\leq n

for all

x\in S

; II. the product of all elements in

S

is the square of an integer.