Mathematics in Education, Research and Applications (MERAA), 2019(5), 2

Published online 20191201
DOI:https://doi.org/10.15414/meraa.2019.05.02.5360
Development and prospects of Stewart’s theorem research
Olena Melnichenko, Uliana Revytska
Bila Tserkva National Agrarian University, Department of Mathematics and Physics, Ukraine
Article Fulltext (PDF), pp. 53–60
 This paper is devoted to the study of Stewart's theorem, its consequences, development and prospects of research of the
theorem under consideration. The paper focuses on the Diophantine equations and their relation to the Stewart’s theorem. The
problem of determination of integer solutions of the Diophantine equations was considered, and some modern researches of the
Stewart’s theorem are presented from the point of view of finding integer solutions of it, which are related to the first and second
order Diophantine equations. The wellknown integer solutions of the Stewart’s theorem, and the definitions, which have been
formulated in the form of a table, are presented in this paper. Some practical applications of the Stewart’s theorem focused on
computing the length of a segment, that connects the vertex of a triangle with its inner point, are relevant in the area of logistics,
management and designing.
 Keywords: triangle geometry, Stewart’s theorem, Diophantine equations, integer solutions
 JEL Classification: C02, C30