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Problem 2 of Second round

Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade

September 22, 2018
number theoryDivisorsgreatest common divisor

Problem Statement

n>1n > 1 is an odd number and a1,a2,...,ana_1, a_2, . . . , a_n are positive integers such that gcd(a1,a2,...,an)=1gcd(a_1, a_2, . . . , a_n) = 1. If
d=gcd(a1n+a1.a2...an,a2n+a1.a2...an,...,ann+a1.a2...an)d = gcd (a_1^n + a_1.a_2. . . a_n, a_2^n + a_1.a_2. . . a_n, . . . , a_n^n + a_1.a_2. . . a_n)
find all possible values of dd.
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