Integral points in arithmetic progression on \(y^2= x(x^2-n^2)\)

DOI10.1006/jnth.1999.2430zbMath1009.11035OpenAlexW2077954256MaRDI QIDQ1971700

Joseph H. Silverman, Nicholas Tzanakis, Andrew Bremner

Publication date: 29 April 2003

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1999.2430

zbMATH Keywords

elliptic curvesarithmetic progressions

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05)

Related Items (22)

Elliptic divisibility sequences over certain curves ⋮ Multiples of integral points on elliptic curves ⋮ Searching for simultaneous arithmetic progressions on elliptic curves ⋮ On the equation \(y^2=x(x - 2^m)(x+q - 2^m)\) ⋮ Integral points on the congruent number curve ⋮ On arithmetic progressions in recurrences -- a new characterization of the Fibonacci sequence ⋮ Markoff-Rosenberger triples in geometric progression ⋮ Arithmetic progressions on Pell equations ⋮ Arithmetic progressions on congruent number elliptic curves ⋮ On certain Diophantine equations of the form \(z^2=f(x)^2\pm g(y)^2\) ⋮ Height estimates on cubic twists of the Fermat elliptic curve ⋮ On the elliptic curve \(y^2= x^3-2rDx\) and factoring integers ⋮ Prime power terms in elliptic divisibility sequences ⋮ Unnamed Item ⋮ Primitive divisors of elliptic divisibility sequences ⋮ A quantitative primitive divisor result for points on elliptic curves ⋮ SIMULTANEOUS ARITHMETIC PROGRESSIONS ON ALGEBRAIC CURVES ⋮ Practical solution of the Diophantine equation $y^2 = x(x+2^ap^b)(x-2^ap^b)$ ⋮ Primitive Divisors on Twists of Fermat's Cubic ⋮ Integral points on the elliptic curve $y^2=x^3-4p^2x$ ⋮ LANG'S CONJECTURE AND SHARP HEIGHT ESTIMATES FOR THE ELLIPTIC CURVES y² = x³ + ax ⋮ On arithmetic progressions on Edwards curves

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