MathDB

3

Part of 2002 Vietnam Team Selection Test

Problems(1)

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

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

6/26/2005
Let mm be a given positive integer which has a prime divisor greater than 2m+1\sqrt {2m} +1 . Find the minimal positive integer nn such that there exists a finite set SS of distinct positive integers satisfying the following two conditions: I. m≤x≤nm\leq x\leq n for all x∈Sx\in S; II. the product of all elements in SS is the square of an integer.
number theory unsolvednumber theory