A unique pair of triangles

Yoshinosuke Hirakawa, Hideki Matsumura

研究成果: Article査読

9 被引用数 (Scopus)

抄録

A rational triangle is a triangle with sides of rational lengths. In this short note, we prove that there exists a unique pair of a rational right triangle and a rational isosceles triangle which have the same perimeter and the same area. In the proof, we determine the set of rational points on a certain hyperelliptic curve by a standard but sophisticated argument which is based on the 2-descent on its Jacobian variety and Coleman's theory of p-adic abelian integrals.

本文言語English
ページ(範囲)297-302
ページ数6
ジャーナルJournal of Number Theory
194
DOI
出版ステータスPublished - 1月 2019

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