• Parametric Equations Giving Solution Sets Memorial Conjecture

    Remzi AKTAY

    Çubuk Science and Art School.

    Abstract: It was proposed by Paul Erdös in 1948 and known as the Erdos-Strauss Delusion guess that for a positive integer P ≥2, the sum of three positive unit fractions is     and the solution sets are always. So far the proof for every positive integer P could not be done. So far,with the help of computer programs, it has been found that this second is satisfied up to . This study, it is aimed to find the parametric equations that give the solution sets for positive integers P. Quantitative research methods  and experimental designs in this method were used in this study. The topics of rational equations, identities and first-order equations with two unknowns were used in the study.  The positive integers P were divided into three groups and these groups were analyzed separately as even numbers P, prime numbers P and odd numbers P, respectively. From the sets of non-prime odd numbers that give a remainder when divided by 3 for the positive integers P, it was found that the solution sets for the numbers that give a remainder when divided by , parametric equations that give solution sets for all P numbers except for some P numbers whose factors  all give a remainder when divided by 3, was  found.All parametric equations found are equations that do not exist in the literature. Based on this study, new studies can be conducted for the set of numbers for which parametric equations cannot be found.İf parametric equations satisfying this set of numbers can be found, the conjecture will be completely proved.

    Keywords: Erdös Strauss Delusion, Parametric Equations, Number theory , Algebra.

    Pages: 71 – 87 | Full PDF Paper