Integers with neighbouring digits differing by one (BxMO 2023, Problem 4)
Source: BxMO 2023, Problem 4
May 6, 2023
BxMOnumber theory
Problem Statement
A positive integer is friendly if the difference of each pair of neighbouring digits of , written in base , is exactly . For example, 6787 is friendly, but 211 and 901 are not.Find all odd natural numbers for which there exists a friendly integer divisible by .