Four rational squares in arithmetic progressions and a family of elliptic curves with positive Mordell-Weil rank-Reference-Cited by-同舟云学术

Four rational squares in arithmetic progressions and a family of elliptic curves with positive Mordell-Weil rank

Published:2020-06-30 Issue:2 Volume:67 Page:213-236
ISSN:0720-728X
Container-title:Mathematische Semesterberichte
language:en
Short-container-title:Math Semesterber

Author:

Knaf Hagen,Selder Erich,Spindler Karlheinz

Abstract

Abstract We study the question at which relative distances four squares of rational numbers can occur as terms in an arithmetic progression. This number-theoretical problem is seen to be equivalent to finding rational points on certain elliptic curves. Both number-theoretical results and results concerning the associated elliptic curves are derived; i.e., the correspondence between rational squares in arithmetic progressions and elliptic curves is exploited both ways.

Funder

Hochschule RheinMain

Publisher

Springer Science and Business Media LLC

Subject

General Mathematics

Link

http://link.springer.com/content/pdf/10.1007/s00591-020-00279-z.pdf

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