1 citations · 1 across the 10 of their papers we have counts for
10 papers
The Seventeen Elements of Pythagorean Triangles
Konstantine Zelator
This is an exhaustive study of the seventeen elements of Pythagorean triangles, from the point of view of when such an element is an irrational number, a rational number, or an int…
A simple method for generating rational triangles
Konstantine Zelator
In the early part of the paper, various geometrical formulas are derived. Then, at some point in the paper, the concept of a Pythagorean rational is introduced. A Pythagorean ratio…
On a Theorem on sums of the form 1+2^(2^n)+2^(2^n+1)+...+2^(2^n+m) and a result linking Fermat with Mersenne numbers
Konstantine "Hermes" Zelator
In his book "250 Problems in Elementary Number Theory", W.Sierpinski shows that the numbers 1+2^(2^n)+2^(2^n+1) are divisible by 21; for n=1,2,.... In this paper, we prove a simila…
Lattice points on the plane ax+by+cz=d and the diophantine system ax+by+cz=d ex+fy+gz=h
Konstantine Zelator
The subject matter of this work are the linear, three variable diophantine equation ax+by+cz=d (1), and the diophantine system ax+by+cz=d (2) ex+fy+gz=h with the coefficients a,b,c…
Two Theorems on the structure of Pythagorean triples and some diophantine consequences
Konstantine "Hermes" Zelator
Even though four theorems are actually proved in this paper, two are the main ones,Teorems 1 and 3. In Theorem 1 we show that if a and be are odd squarefree positive integers satis…
Heron isosceles with integral external radii
Konstantine Zelator
Each triangle has three exterior or external circles tangential to the three straight lines containing the three sides of the triangle.Among the preliminaries in this paper, is der…