Asian Journal of Pure and Applied Mathematics

The Congruent Number Problem

Jan Feliksiak *

Language School in Krakw, Poland.

*Author to whom correspondence should be addressed.

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Abstract

The congruent number problem is the oldest unsolved major mathematical problem to date. The problem aiming to determine whether or not some given integer n is congruent, which corresponds to a Pythagorean triangle with integer sides, can be settled in a finite number of steps. However, once we permit the triangles to acquire rational values for its sides, the degree of diffculty of the task changes dramatically. In this paper a basis is developed, to produce right Pythagorean triangles with rational sides and integral area in a straightforward manner. Determining whether or not a given natural number n is congruent, is equivalent to a search through an ordered 2D array.

Keywords: Leaf extracts, Babylonian mathematics, effect, Effect of Parthenium, congruent number problem, Stomatal features, homogeneous Diophantine equations, Euclid's parametrization, rational Pythagorean triples

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