DIOPHANTE'S SPECIAL CASE EQUATION - Zulhumor Amatovna Tangirova (Galaxy International Interdisciplinary Research Journal, 2022)
Diophantine equations - algebraic equations with two or more unknowns, whose coefficients are integers; in which solutions consisting of whole or rational numbers are sought. The general theory of the first-order D. t. was created by the French mathematician Bashe, who lived in the 17th century. As a result of research by Fermat, Euler, Lagrange and Gauss at the beginning of the 19th century, the second order D. t. was mainly investigated. The methods of checking D. t. are based on the theory of continuous fractions. D. t. also means systems of algebraic equations with integer coefficients in which the number of unknowns is greater than the number of equations. D. t., sometimes referred to as indeterminate equations.