infinite m = n^2+ n + 1 with pefect square factors
Source: China Northern MO 2023 p6 CNMO
May 5, 2024
number theoryPerfect SquaresPerfect Square
Problem Statement
A positive integer is called a beautiful integer if that there exists a positive integer such that . Prove that there are infinitely many beautiful integers with square factors, and the square factors of different beautiful integers are relative prime.