MathDB
Oeirense numbers

Source: Lusophon Mathematical Olympiad 2024 Day 2 Problem 6

July 26, 2024
number theory

Problem Statement

A positive integer nn is called oeirenseoeirense if there exist two positive integers aa and bb, not necessarily distinct, such that n=a2+b2n=a^2+b^2.
Determine the greatest integer kk such that there exist infinitely many positive integers nn such that nn, n+1n+1, \dots, n+kn+k are oeirenses.