At least one of 2k-1, 5k-1, 13k-1 is not a perfect square
Source: Cyprus 2022 Junior TST-3 Problem 1
March 26, 2022
number theoryPerfect Square
Problem Statement
Prove that for every natural number , at least one of the integers
2k-1, 5k-1 \text{and} 13k-1
is not a perfect square.