期刊论文

英文

Functiones et Approximatio Commentarii Mathematici

0208-6573

2023

69

1

43-54

10.7169/facm/2031

This research was supported by the National Natural Science Foundation of China (Grant No. 11501052), the Natural Science Foundation of Hunan Province (Project No. 2021JJ30699), Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering (Changsha University of Science and Technology) and the Natural Science Foundation of Zhejiang Province (Project No. LY18A010016).

本校为第一机构

Suppose that the rational right triangle triple is (T1, T2, T3), their areas are Ai (i = 1, 2, 3), and perimeters are Pi (i = 1, 2, 3). By the theory of elliptic curves, we investigate the solvability of the following Diophantine system A1 + αA2 = βA3, P1 + αP2 = βP3, where α and β are rational numbers. When (α, β) = (−2, −1) or (α, β) = (1, 1), we show that there are infinitely many rational right triangle triples with the same perimeter and the areas in arithmetical progression or with the areas and perimeters satisfying the linea...