The Congruent Number Problem
Jan Feliksiak *
Language School in Krakw, Poland.
*Author to whom correspondence should be addressed.
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