MathDB
Putnam 1973 A3

Source: Putnam 1973

May 25, 2022
Putnamfloor functioninequalitiesminimum

Problem Statement

Let nn be a fixed positive integer and let b(n)b(n) be the minimum value of k+nk,k+\frac{n}{k}, where kk is allowed to range through all positive integers. Prove that b(n)=4n+1.\lfloor b(n) \rfloor= \lfloor \sqrt{4n+1} \rfloor.