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Linear and quadratic sum of digits property

Source: Germany Bundeswettbewerb Mathematik 2007, Round 2, Problem 1

July 18, 2008
quadraticsinductionnumber theory unsolvednumber theory

Problem Statement

For which numbers n n is there a positive integer k k with the following property: The sum of digits for k k is n n and the number k2 k^2 has sum of digits n2. n^2.
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