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Moldova TST, greatest prime divisor of the sum

Source: Moldova TST 2014, First Day, Problem 4

March 4, 2014
AMCAIMEnumber theory proposednumber theory

Problem Statement

Define p(n)p(n) to be th product of all non-zero digits of nn. For instance p(5)=5p(5)=5, p(27)=14p(27)=14, p(101)=1p(101)=1 and so on. Find the greatest prime divisor of the following expression: p(1)+p(2)+p(3)+...+p(999).p(1)+p(2)+p(3)+...+p(999).
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