ALGEBRAIC POINTS OF DEGREE AT MOST 14 ON THE FERMAT SEPTIC

ALGEBRAIC POINTS ON THE FERMAT SEPTIC

Abstract

In this paper, we study the algebraic points of degree at most 14 over Q on the Fermat septic
curve F7 of projective equation X⁷ + Y ⁷ + Z⁷ = 0. Klassen and Tzermias gave in 1997 in ([5]) a geometric
description of algebraic points of degree at most 5 over Q on F₇ and O. Sall improved the results of Klassen
and Tzermias by determining in 2001 in ([9]), the algebraic points of degree at most 10 over Q. Using their
results and Abel Jacobi's theorem, we extend their work by giving a geometric description of algebraic points
of degree at most 14 over Q on F₇.