MathDB
JBMO Shortlist 2023 N2

Source: JBMO Shortlist 2023, N2

June 28, 2024
JBMOJBMO Shortlistnumber theory

Problem Statement

A positive integer is called Tiranian if it can be written as x2+6xy+y2x^2+6xy+y^2, where xx and yy are (not necessarily distinct) positive integers. The integer 36202336^{2023} is written as the sum of kk Tiranian integers. What is the smallest possible value of kk?
Proposed by Miroslav Marinov, Bulgaria