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n = S(n) + P(n), sum , product digits (HOMC 2018 ind. sen13)

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February 2, 2020
sum of digitsProductDigitsnumber theorySum

Problem Statement

For a positive integer nn, let S(n),P(n)S(n), P(n) denote the sum and the product of all the digits of nn respectively. 1) Find all values of n such that n=P(n)n = P(n): 2) Determine all values of n such that n=S(n)+P(n)n = S(n) + P(n).
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