This paper presents a complete and exhaustive proof of the Beal Conjecture. The approach to this proof uses the Fundamental Theorem of Arithmetic as the basis for the proof of the Beal Conjecture. The Fundamental Theorem of Arithmetic states that every number greater than 1 is either prime itself or is unique product of prime numbers. The prime factorization of every number greater than 1 is used throughout every section of the proof of the Beal Conjecture. Without the Fundamental Theorem of Arithmetic, this approach to proving the Beal Conjecture would not be possible.
The Bulletin of Society for Mathematical Services and Standards (Volume 7)
S. M. Marshall "An All-Inclusive Proof of Beal’s Conjecture", The Bulletin of Society for Mathematical Services and Standards, Vol. 7, pp. 17-22, 2013