MathDB
Double Numbers

Source: Turkey TST 1989 - P2

September 11, 2013
number theory proposednumber theory

Problem Statement

A positive integer is called a "double number" if its decimal representation consists of a block of digits, not commencing with 00, followed immediately by an identical block. So, for instance, 360360360360 is a double number, but 3603636036 is not. Show that there are infinitely many double numbers which are perfect squares.