Open AccessOn the Solutions of Diophantine Equation (Mp − 2) x + (Mp + 2) y = z 2 where Mp is Mersenne Prime
Author(s) -
Vipawadee Moonchaisook
Publication year - 2021
Publication title -
international journal of basic sciences and applied computing
Language(s) - English
Resource type - Journals
ISSN - 2394-367X
DOI - 10.35940/ijbsac.d0216.083421
Subject(s) - mersenne prime , diophantine equation , prime (order theory) , mathematics , mathematical proof , prime number , variety (cybernetics) , discrete mathematics , pure mathematics , combinatorics , statistics , geometry
The Diophantine equation has been studied by many researchers in number theory because it helps in solving variety of complicated puzzle problems. From several studies, many interesting proofs have been found. In this paper, the researcher has examined the solutions of Diophantine equation ( − ) + ( + ) = where is a Mersenne Prime and p is an odd prime whereas x, y and z are nonnegative integers. It was found that this Diophantine equation has no solution.