MathDB

[ \sqrt{n} ] + [ n / [ \sqrt{n} ] ] > 2 \sqrt{n}

Source: (2022 -) 2023 XVI Dürer Math Competition Regional E+1

May 25, 2024

algebrainequalitiesfloor function

Problem Statement

Find all positive integers

n

such that

\lfloor \sqrt{n} \rfloor + \left\lfloor \frac{n}{\lfloor \sqrt{n} \rfloor} \right \rfloor> 2\sqrt{n}.

k

is a real number, then

\lfloor k \rfloor

means the floor of

k

, this is the greatest integer less than or equal to

k