The solution of the Diophantine equation x^2+3y^2=z^2

Abstract

In this paper we are interested to show how to solve the diophantine equation x 2 + 3y 2 = z 2 by using the arithmetic technical.

The Primitive-Solutions of Diophantine Equation x^2+pqy^2=z^2, for primes p,q

“…On this paper, we extend the results of [1], [6] and [8] to determine the primitive-solutions of Diophantine equation where , and are positive integers, and and are primes. We establish results that the equation for case is odd has no primitive-solution and case is even have two primitive-solutions.…”

“…Next, there are Abdealim and Dyani [1] who had given the solutions for case of by using the arithmetic technical. Following this, Rahman and Hidayat [6] presented the primitivesolutions for case of using characteristics of the primitive solutions which are a development of the previous cases.…”

Lattice equable quadrilaterals I: Parallelograms

“…We will also require the following classical result. There are several proofs of this result; a direct, elementary proof is given in [1].…”

“…, where x n = 6w n + 3. Note that the vertical side OA n has length a := 4 √ 3, while the side OC n has length 3 lists the first six examples of ELEPs corresponding to the sequence with initial condition (w 1 , y 1 ) = (1,13). The first five of these ELEPs appear in Figure 7 in the branch that starts at the element (a, b) = (4, 14) and proceeds horizontally to the right.…”