A SUMMARY OF AN EXTENSIVE ESSAY ON THE THEME OF:

The Beal Conjecture: A^x + B^y = C^z

A Proof and Counterexamples [A^x + B^y = z^C]

Charles William Johnson

The conjecture A^x + B^y = C^z made by Mr. Andrew Beal is concerned with the common prime factor for positive integers and their exponents.

The Beal Conjecture requires positive integers in the terms [A, B, C] and exponents [x, y, z] of the equation (the latter whose value must be greater than 2). The products of the terms must reflect the selfsame multiplication of the terms in whole numbers or positive integers. Obviously, no fractional expressions are to appear in any of the three terms or three exponents of the equation. And, the most significant part of the conjecture affirms the necessity that the terms share a common prime divisor. Or, to the contrary, present counterexamples.

Terms with a common prime divisor produce whole number terms with whole number multiples (exponents). Terms without a common prime divisor produce whole number terms and whole number multiples but fractional proportions among the multiples. Terms without a common prime divisor with whole number terms and whole number exponents with whole number proportions among the multiples do not exist.........

If the difference between selfsame addition and selfsame multiplication were commonly perceived, then one would not propose the idea of counterexamples through selfsame multiplication, knowing the infinite number of counterexamples in selfsame addition. Furthermore, today's algebraic notation concentrates upon selfsame multiples through multiplication, which is an extremely limited number of possible relations of equivalency, a fraction of the possibilities attainable through selfsame addition. For a more exhaustive treatment of any mathematical subject, we should be teaching our students selfsame addition, which embraces the total universe of possibilities in these analyses.

Jefferson, Louisiana
22 August 2002

THE GOLDBACH CONJECTURE AND THE UNIVERSE OF PRIMES

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Book: THE GOLDBACH CONJECTURE AND THE UNIVERSE OF PRIMES The Goldbach Conjecture and the Universe of Primes examines the even-sum tables of the natural numbers and prime numbers in proving the conjecture. The explanation of the inner workings of the Goldbach conjecture are rendered into simple math. Knowing how to add is all that is required. Profusely illustrated with easy-to-read math tables explaining how the sum of primes perform in relation to the conjecture. The author examines the Goldbach Conjecture, a 262 year-old conjecture. It is impossible to prove the Goldbach Conjecture in the manner in which the theorists of mathematics have been demanding. Instead of a resolution based on algebra, an explanation of the Goldbach Conjecture based on the numbers is required. In fact, this may be a simpler task than imagined until now. Purchase in Amazon The Goldbach Conjecture and the Universe of Primes Author: Charles William Johnson 182 pages Price $7.99 US You can purchase: click

Earth/matriX Editions

Earth/matriX:
Science in Ancient Artwork and Science Today
A SUMMARY OF THE ESSAY: ISBN 58616-327-2
August 2002
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