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P (m+P(m) )= P (m) where P is product of digits

Source: Mathematics Regional Olympiad of Mexico West 2020 P4

September 10, 2022
number theoryproduct of digits

Problem Statement

Given a positive integer n n , we denote by P(n) P(n) the result of multiplying all the digits of n n . Find a number m m with ten digits, none of them zero, with the following property: P(m+P(m))=P(m)P\left(m+P(m)\right)= P (m)