MathDB

NT inequality, number of digits

Source: Yugoslav TST 1970 P1

May 30, 2021

inequalitiesnumber theory

Problem Statement

Positive integers

a

and

b

have

n

digits each in their decimal representation. Assume that

m

is a positive integer such that

\frac n2<m<n

and assume that each of the leftmost

m

digits of

a

is equal to the corresponding digit of

b

. Prove that

a^{\frac1n}-b^{\frac1n}<\frac1n.