MathDB

18

Part of 2017 Baltic Way

Problems(1)

Permutation and residues

Source: Baltic Way 2017 Problem 18

11/11/2017
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?
number theoryabstract algebra