MathDB
Polynomial

Source: Baltic Way 2015

November 8, 2015
polynomialalgebranumber theory

Problem Statement

Denote by P(n)P(n) the greatest prime divisor of nn. Find all integers n2n\geq 2 for which P(n)+n=P(n+1)+n+1P(n)+\lfloor\sqrt{n}\rfloor=P(n+1)+\lfloor\sqrt{n+1}\rfloor