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The sum of digits

Source: Problem 4 from ZIMO 2008

January 21, 2008
inequalitiesmodular arithmeticnumber theory proposednumber theory

Problem Statement

For each positive integer n n,denote by S(n) S(n) the sum of all digits in decimal representation of n n. Find all positive integers n n,such that n\equal{}2S(n)^3\plus{}8.
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