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Cyclic Expression Equals Two

Source: Indian RMO 2013 Paper 1 Problem 4

February 1, 2014

modular arithmeticcombinatorics unsolvedcombinatorics

Problem Statement

Find the number of

10

-tuples

(a_1,a_2,\dots,a_9,a_{10})

of integers such that

|a_1|\leq 1

and

a_1^2+a_2^2+a_3^2+\cdots+a_{10}^2-a_1a_2-a_2a_3-a_3a_4-\cdots-a_9a_{10}-a_{10}a_1=2.