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On arithmetic progressions on Edwards curves

Enrique González-Jiménez (2015)

Acta Arithmetica

Let m > 0 and a,q ∈ ℚ. Denote by 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 x ² y ² . We study the set m ( a , q ) and we parametrize it by the rational points of an algebraic curve.

On subfields of k ( x )

Victor Alexandru, Nicolae Popescu (1986)

Rendiconti del Seminario Matematico della Università di Padova

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