square triple of natural numbers , abc =d^2
Source: Russian Regional Olympiad 2010 11.4
August 24, 2024
number theoryPerfect Square
Problem Statement
We call a triple of natural numbers square if they form an arithmetic progression (in exactly this order), the number is coprime to each of the numbers and , and the number is a perfect square. Prove that for any given a square triple, there is another square triple that has at least one common number with it.