Add to ORKGAbstract. We discuss the problem of nding integer-sided triangles with the ratio base/altitude or altitude/base an integer. This problem is mentioned in Richard Guy's book "Unsolved Problems in Number Theory". The problem is shown to be equivalent to nding rational points on a family of elliptic curves. Various computa-tional resources are used to nd those integers in [1; 99] which do appear, and also nd the sides of example triangles. A.M.S. (MOS) Subject Classication Codes. 11D25, 11Y5
Abstract. We combine various well-known techniques from the theory of heights, the theory of “noncri...
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geo...
AbstractWe present a characterization of all rational sided triangles with three rational medians. I...
AbstractWe consider the problem of finding two integer right-angled triangles, having a common base,...
AbstractWe consider the problem of finding two integer right-angled triangles, having a common base,...
This paper explores the congruent number problem, which asks which rational numbers are areas of tri...
Abstract. A natural number is called a congruent number if it is the area of a right triangle with r...
The correspondence between right triangles with rational sides, triplets of rational squares in arit...
The correspondence between right triangles with rational sides, triplets of rational squares in arit...
We combine various well-known techniques from the theory of heights, the theory of “noncritical Bel...
Abstract. Let C be an affine, plane, algebraic curve of degree d with integer coefficients. In 1989,...
Throughout this thesis we will be primarily concerned with the area of a rational right angle triang...
Abstract. We show that the number of rational points of height ≤ H on a non-rational plane curve of ...
Abstract. We show that the number of rational points of height ≤ H on a non-rational plane curve of ...
In the July 2018 issue of At Right Angles, author A S Rajagopalan had explored the number of tri...
Abstract. We combine various well-known techniques from the theory of heights, the theory of “noncri...
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geo...
AbstractWe present a characterization of all rational sided triangles with three rational medians. I...
AbstractWe consider the problem of finding two integer right-angled triangles, having a common base,...
AbstractWe consider the problem of finding two integer right-angled triangles, having a common base,...
This paper explores the congruent number problem, which asks which rational numbers are areas of tri...
Abstract. A natural number is called a congruent number if it is the area of a right triangle with r...
The correspondence between right triangles with rational sides, triplets of rational squares in arit...
The correspondence between right triangles with rational sides, triplets of rational squares in arit...
We combine various well-known techniques from the theory of heights, the theory of “noncritical Bel...
Abstract. Let C be an affine, plane, algebraic curve of degree d with integer coefficients. In 1989,...
Throughout this thesis we will be primarily concerned with the area of a rational right angle triang...
Abstract. We show that the number of rational points of height ≤ H on a non-rational plane curve of ...
Abstract. We show that the number of rational points of height ≤ H on a non-rational plane curve of ...
In the July 2018 issue of At Right Angles, author A S Rajagopalan had explored the number of tri...
Abstract. We combine various well-known techniques from the theory of heights, the theory of “noncri...
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geo...
AbstractWe present a characterization of all rational sided triangles with three rational medians. I...