UNIQUE FACTORIZATION, FERMAT’S LAST THEOREM, BEAL’S CONJECTURE

  • James Joseph Department of Mathematics Howard University
Keywords: Fermat's Last Theorem, Beal's Conjecture

Abstract

In this paper the following statememt of Fermat\rq{}s Last Theorem is proved.  If  $x, y, z$ are positive integers$\pi$ is an odd prime and  $z^\pi=x^\pi+y^\pi, x, y, z$ are all even. Also, in this paper, is proved (Beal\rq{}s conjecture): The equation $z^\xi=x^\mu+y^\nu$ has no solution in relatively prime positive integers $x, y, z, $ with $\xi, \mu, \nu$ primes at least $3.

Author Biography

James Joseph, Department of Mathematics Howard University
department of Mathematics, Retired Professor

References

H. Edwards, {it Fermat's Last Theorem:A Genetic Introduction

to Algebraic Number Theory/}, Springer-Verlag, New York, (1977).

A. Wiles, {it Modular ellipic eurves and Fermat's Last

Theorem/}, Ann. Math. 141 (1995), 443-551.

A. Wiles and R. Taylor, {it Ring-theoretic properties of

certain Heche algebras/}, Ann. Math. 141 (1995), 553-573.

Published
2016-11-16
How to Cite
Joseph, J. (2016). UNIQUE FACTORIZATION, FERMAT’S LAST THEOREM, BEAL’S CONJECTURE. Journal of Progressive Research in Mathematics, 10(1), 1434-1439. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/936
Section
Articles