| property."The Fermat Little Theorem, with extended hint", a proof by Brian S. McMillan. IF: (2^(P-1)-1)/P = Integer, Fermat c 1650 WHERE: P = Prime or Pseudo-Prime AND: (2^(P-1)-1)/P = N (PN±2) McMillan c2003 THEN: (2^((P-1)/2) ±1)/P = N Integer The last two equations above completes the proof. However, since an algebraic proof in its most simple terms, has never been provided, since Fermat was in the habit of not providing any, saying he would except-for fear of it being to long. And, since the proof that I have discovered is so brief, and in its simplest terms, it is highly unlikely that Fermat ever had one! These equations provide proof for the Twin- Primes Conjecture and a host of other related conjectures, including the Fermat Conjecture above; It can now be called a theorem! The following equation is useful in that the fidelity of the original Fermat equation is maintained through a yield of the integer for Pseudo-Primes and Prime "P" or the fraction for Non-Primes. HENCE: (2^((P-1)/2) -P(N-1) ±1)/P = 1 In the last equation, N can be any number at all, as long as its an integer. My name is Brian S. McMillan, I discovered this, I AM LUCKY MAN Santa Rosa California. PS. I have continued the liberty of using the smallest base "2" as this is the most popular base of choice. I have, therefore, only provided an informal proof and a more formal one can be provided on request. I have also been working on a wonderful proof for the Wilson Theorem. Thank You for your attention in this matter. PSS. Hint: Some programs such a "Beginner's All-purpose Symbolic Instruction Code" or BASIC, have the option of removing the mantissa. In this case the algorythm yielding N, may be inserted inside the final equation above, with the mantissa removed using a command at the address prior to insertion. This will always yield a one+- a fraction for non-primes or one for primes and pseudo-primes, no matter how large the prime exponent is... FANTASTIC! SIGNED: Brian S. McMillan PPSS. Application of the computer BASIC "cheat" to the original Little Fermat Equation; where the "INT" command is applied to a duplicate formula in the denominator creating a differential equation... would be the easiest way to kick out primes... but then a good old fasioned proof would not have been presented! Hope you like it... really. Oh yea, if you really want to get to the bottom of things, use the "cheat" with the Wilson Theorem... No pseudo-primes! THEORY: Since "nothing" can exist in "less or more" than 3-dimensions (at least, not so far as anyone has been able to prove) and material volume is measured in the dimensions of x,y,z; that is, it has height, width and depth. This is measured as a solid, liquid, gas or plasma of any fundamental unit of the material to be measured, and this, in relation to a finite bounded volume. This might be why it is not possible to find an exponent greater than 2 as a solution to the more famous "Fermat's Last Theorem"... as it would be alot like trying to "Square a Circle". Since the 2-dimensional surface area of any designated length involves the "Squaring" of that particular dimensional measurement. And this "Area" is directly related to a "Surface" or real estate of actual physical | |
|
