MathDB

Prove that among

20

consecutive positive integers there is an integer

d

such that for every positive integer

n

the following inequality holds

n \sqrt{d} \left\{n \sqrt {d} \right \} > \dfrac{5}{2}

where by

\left \{x \right \}

denotes the fractional part of the real number

x

. The fractional part of the real number

x

is defined as the difference between the largest integer that is less than or equal to

x

to the actual number

x

.
(Serbia)

Problem Statement