Andrew Bremner
Abstract
Open-access reader
We study arithmetic progressions in the x-coordinates of rational points on elliptic curves. An infinite family of elliptic curves is found, each containing an arithmetic progression of length 8.
OpenAlex reports 39 citations for this work. Citation counts describe recorded attention and do not establish research quality.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
We study arithmetic progressions in the x-coordinates of rational points on elliptic curves. An infinite family of elliptic curves is found, each containing an arithmetic progression of length 8.
Key concepts: Mathematics, Elliptic curve, Arithmetic, Hessian form of an elliptic curve, Supersingular elliptic curve, Schoof's algorithm, Division polynomials, Elliptic curve point multiplication