On the Integer Solution of the Transcendental Equation

Abstract

Let C be a positive non-square integer. In this paper, we look at the complete solutions of the Transcendental equation √𝟐𝒛−𝟒=√𝒙+√𝑪𝒚± √𝒙−√𝑪𝒚 , where 𝒙𝟐−𝑪𝒚𝟐=𝜶𝟐 or 𝟐𝟐𝒕. In addition, we find repeated relationships in the solutions to this figure.