MathDB
product - sum is a perfect sqaure

Source: Vietnam TST 2002 for the 43th IMO, problem 6

June 26, 2005
number theory unsolvednumber theory

Problem Statement

Prove that there exists an integer nn, n≥2002n\geq 2002, and nn distinct positive integers a1,a2,…,ana_1,a_2,\ldots,a_n such that the number N=a12a22⋯an2−4(a12+a22+⋯+an2)N= a_1^2a_2^2\cdots a_n^2 - 4(a_1^2+a_2^2+\cdots + a_n^2) is a perfect square.
Back to ProblemsView on AoPS