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Permutation and residues

Source: Baltic Way 2017 Problem 18

November 11, 2017
number theoryabstract algebra

Problem Statement

Let p>3p>3 be a prime and let a1,a2,...,ap−12a_1,a_2,...,a_{\frac{p-1}{2}} be a permutation of 1,2,...,p−121,2,...,\frac{p-1}{2}. For which pp is it always possible to determine the sequence a1,a2,...,ap−12a_1,a_2,...,a_{\frac{p-1}{2}} if it for all i,j∈{1,2,...,p−12}i,j\in\{1,2,...,\frac{p-1}{2}\} with i≠ji\not=j the residue of aiaja_ia_j modulo pp is known?
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