MathDB

13

Part of 2019 Latvia Baltic Way TST

Problems(1)

Infinitely many integers satisfying inequality with sum of digits of number

Source: Latvian TST for Baltic Way 2019 Problem 13

5/29/2020
Let s(k)s(k) denotes sum of digits of positive integer kk. Prove that there are infinitely many positive integers nn, which are not divisible by 1010 and satisfies: s(n2)<s(n)āˆ’5s(n^2) < s(n) - 5
inequalitiesnumber theory