MathDB
4 |n if a_1a_2 + a_2a_3 + ··· + a_{n-1}a_n + a_na_1 = 0, for a_i \in {1,-1}

Source: Portugal OPM 1999 p5

May 18, 2024
number theorySumalgebra

Problem Statement

Each of the numbers a1,...,ana_1,...,a_n is equal to 11 or 1-1. If a1a2+a2a3++an1an+ana1=0a_1a_2 + a_2a_3 + ··· + a_{n-1}a_n + a_na_1 = 0, proves that nn is divisible by 44.