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number twice the square of sum of digits in decimal

Source: RMO Mumbai 2016, P3

October 11, 2016
number theoryinequalities

Problem Statement

For any natural number nn, expressed in base 1010, let S(n)S(n) denote the sum of all digits of nn. Find all natural numbers nn such that n=2S(n)2n=2S(n)^2.
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