find all nice ones
Source: ItaMO 2009, p3
February 22, 2012
number theory proposednumber theory
Problem Statement
A natural number is called nice if it enjoys the following properties:
• The expression is made up of decimal digits;
• the first and third digits of are equal;
• the second and fourth digits of are equal;
• the product of the digits of divides .
Determine all nice numbers.