Problem

Source: OLCOMA (Costa Rican MO) Shortlist, 2017

Tags: number theory, Digits



A positive integer is said to be "nefelibata" if, upon taking its last digit and placing it as the first digit, keeping the order of all the remaining digits intact (for example, 312 -> 231), the resulting number is exactly double the original number. Find the smallest possible nefelibata number.