MathDB

Turkey Junior Olympiad 2000, Part II - P2

Source:

January 18, 2013

modular arithmetic

Problem Statement

Find the least positive integer

n

such that

15

divides the product

a_1a_2\dots a_{15}\left (a_1^n+a_2^n+\dots+a_{15}^n \right )

, for every positive integers

a_1, a_2, \dots, a_{15}