erasing first digits in natural numbers written in the decimal system
Source: Spanish Mathematical Olympiad 1984 P7
August 2, 2018
number theorydecimal representationDigit
Problem Statement
Consider the natural numbers written in the decimal system.
(a) Find the smallest number which decreases five times when its first digit is erased. Which form do all numbers with this property have?
(b) Prove that there is no number that decreases times when its first digit is erased.
(c) Find the necessary and sufficient condition on for the existence of a natural number which is divided by when its first digit is erased.