MathDB

Infinitely many integers satisfying inequality with sum of digits of number

Source: Latvian TST for Baltic Way 2019 Problem 13

May 29, 2020

inequalitiesnumber theory

Problem Statement

Let

s(k)

denotes sum of digits of positive integer

k

. Prove that there are infinitely many positive integers

n

, which are not divisible by

10

and satisfies:

s(n^2) < s(n) - 5