MathDB

Bounding difference of fractional parts.

Source: Romania TST 2013 Day 3 Problem 1

January 21, 2015

inequalitiesalgebrapolynomialabsolute valuetriangle inequalitynumber theory unsolvednumber theory

Problem Statement

Let

a

and

b

be two square-free, distinct natural numbers. Show that there exist

c>0

such that

\left | \{n\sqrt{a}\}-\{n\sqrt{b}\} \right |>\frac{c}{n^3}

for every positive integer

n