On arithmetic progressions on Edwards curves

Published 16 Apr 2013 in math.NT and math.AG | (1304.4361v2)

Abstract: Let m be a positive integer and a,q two rational numbers. Denote by AP_m(a,q) the set of rational numbers d such that a,a+q,...,a+(m-1)q form an arithmetic progression in the Edwards curve E_d:x^{2+y^2=1+d} x² y^2. We study the set AP_m(a,q) and we parametrize it by the rational points of an algebraic curve.

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Authors (1)

Enrique Gonzalez-Jimenez

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