Un r\'esultat de recherche obtenu gr\^ace \`a des lyc\'eens

TL;DR

This paper provides an elementary proof for a finite field equation solution problem, leveraging results obtained by high school students during a mathematics tournament, highlighting the educational value in advanced mathematical research.

Contribution

The paper introduces an elementary proof of a finite field equation solution, based on results from high school students, bridging education and research in mathematics.

Findings

Elementary proof of the equation solution over finite fields.

Utilization of high school students' results in advanced research.

Demonstrates educational impact on mathematical problem solving.

Abstract

We give an elementary proof of a question asked by Fouvry, Kowalski and Michel on the solutions of the equation $x+\frac{1}{x}+y+\frac{1}{y}+t=0$ over a finite field, using the results obtained by highschool students during their participation at the maths tournament "Tournoi Fran\c{c}ais des Jeunes Math\'ematiciennes et Math\'ematiciens". Nous pr\'esentons une d\'emonstration \'el\'ementaire d'une question pos\'ee par Fouvry, Kowalski et Michel sur les solutions de l'\'equation $x+\frac{1}{x}+y+\frac{1}{y}+t=0$ sur un corps fini, en utilisant des r\'esultats obtenus par des lyc\'eens lors de leur participation au Tournoi Fran\c{c}ais des Jeunes Math\'ematiciennes et Math\'ematiciens.