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On arithmetic progressions on Edwards curves

Enrique González-Jiménez (2015)

Acta Arithmetica

Let $m \in ℤ_{> 0}$ 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 certain Diophantine systems with infinitely many parametric solutions and applications

Maciej Ulas (2010)

Acta Arithmetica

On certain plane curves with many integral points.

Rodriguez Villegas, Fernando, Voloch, José Felipe (1999)

Experimental Mathematics

On symmetric square values of quadratic polynomials

Enrique González-Jiménez, Xavier Xarles (2011)

Acta Arithmetica

On the arithmetic of certain modular curves

Daeyeol Jeon, Chang Heon Kim (2007)

Acta Arithmetica

On the arithmetic of the hyperelliptic curve $y^{2} = x^{n} + a$

Kevser Aktaş, Hasan Şenay (2016)

Czechoslovak Mathematical Journal

We study the arithmetic properties of hyperelliptic curves given by the affine equation $y^{2} = x^{n} + a$ by exploiting the structure of the automorphism groups. We show that these curves satisfy Lang’s conjecture about the covering radius (for some special covering maps).

Displaying 1 – 11 of 11

On arithmetic progressions on Edwards curves

On certain Diophantine systems with infinitely many parametric solutions and applications

On certain plane curves with many integral points.

On symmetric square values of quadratic polynomials

On the arithmetic of certain modular curves

On the arithmetic of the hyperelliptic curve $y^{2} = x^{n} + a$

On the arithmetic of twists of superelliptic curves

On the Diophantine equation $x^{2} + 7 = y^{m}$

On the height constant for curves of genus two

On the height constant for curves of genus two, II

On the number of rational squares at fixed distance from a fifth power

Currently displaying 1 – 11 of 11