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Number theory prob.

Source: Central American Olympiad 2001, problem 4

August 12, 2009

Problem Statement

Determine the smallest positive integer n n such that there exists positive integers a1,a2,⋯ ,an a_1,a_2,\cdots,a_n, that smaller than or equal to 15 15 and are not necessarily distinct, such that the last four digits of the sum, a_1!\plus{}a_2!\plus{}\cdots\plus{}a_n! Is 2001 2001.
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