Problem 5

Part of 2021 Honduras National Mathematical Olympiad

Problems(1)

Honduran National MO (OHM) Intermediate Problem 5

Source: 2021 OHM Intermediate P5

A positive integer

m

is called growing if its digits, read from left to right, are non-increasing. Prove that for each natural number

n

there exists a growing number

m

n

digits such that the sum of its digits is a perfect square.