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Equation of integers

Source: Indonesia Mathematics Olympiad 2005 Day 1 Problem 2

June 2, 2008
number theory proposednumber theory

Problem Statement

For an arbitrary positive integer n n, define p(n) p(n) as the product of the digits of n n (in decimal). Find all positive integers n n such that 11p(n)\equal{}n^2\minus{}2005.
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