ON THE NON HOMOGENEOUS HEPTIC DIOPHANTINE EQUATION (X2- Y2)(8X2 + 8Y2 -14XY) = 19 (X2 –Y2) Z5

THE DIOPHANTINE EQUATION x2+2k =yn, II

New results regarding the full solution of the diophantine equationx2+2k=yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.

ON THE DIOPHANTINE EQUATION x2+p2k+1 = 4yn

ON THE EQUATION x2+2a ·3b =yn

On the System of Diophantine Equations x2 − 6y2 = −5 and x = az2 − b

Mignotte and Pethö used the Siegel-Baker method to find all the integral solutions (x, y, z) of the system of Diophantine equations x (2) - 6y (2) = -5 and x = 2z (2) - 1. In this paper, we extend this result and put forward a generalized method which can completely solve the family of systems of Diophantine equations x (2) - 6y (2) = -5 and x = az (2) - b for each pair of integral parameters a...

Contributions to the Theory of the Non-Central X2 Distribution

In this paper, we consider the probability density function (pdf) of a non-central χ distribution with odd number of degrees of freedom ν. This pdf is represented in the literature as an infinite sum. Consequently, we present three alternative expressions to this pdf. The first expression is in terms of a partial derivative of the hyperbolic cosine function. The second expression, on the other ...