1. M

    Fermat Last Theorem Diophantine Analysis

    Analysis using Diopphantine Equations Diophantine Equations are used to remove as many variables as possible and write the remaining unknowns in terms of the other unknowns. By analyzing the remaining terms as whole numbers, we can decided whether there are infinite number of solutions or zero...
  2. M

    Easy proof of Fermat's last Theorem

    Here is a video I made of a proof of FLT. I have trouble with notation, so I made a YouTube video with handwritten equations and diagrams. 0iCRK41fOQE Enjoy the read.
  3. M

    Fermat's last theorem

    Have I found a novel way of expressing Fermat's last theorem as follows? N = nt{ K.A^(3-p)} where N is the number of primitive triples a, b, c and a^p = b^p +c^p and a all values up to A. (K is about .155, 0.152929 for p =1 and 0.159155 for p = 2) For example, this gives for a up to 10,000...
  4. M

    one page proof of Fermat's Last Theorem

    I am sending you an invitation to see the one page proof of Fermat's Last Theorem. This proof uses Fermat's Right Triangle Theorem to prove the Theorem. Also included in the proof is the diagram Fermat could not include in the margin of the book. It is an amazing proof. wFyX5uqyLLA
  5. R

    A Proof of Fermat's Conjecture

    Hello, Welcoming myself I have a proof of Fermat's Conjecture at: https://www.dropbox.com/s/xxdtksxplf02yaj/%5B1.%20proof%20of%20Fermat%27s%20%28V17FIRM%29%20.pdf?dl=0 within my Dropbox folder at: https://www.dropbox.com/sh/gabop77dlx550wg/AADerU5lqy9yiFKkO0JOExzRa?dl=0 Also...
  6. L

    A stronger fomulation of Fermat's Last Theorem

    We consider only positive integers. The formulation is as follows: Every squared integer can be expressed as the difference of two squared integers; for powers greater than two, there is not a single integer for which an analogous statement is true. In short, every integer is a member...
  7. M

    Mod functions related to Fermat's Last Theorem

    Since Fermat's Last Theorem has been proved, can it be concluded that there can't be three different, relatively prime, non zero integers A>B>C where the following six Mod functions are all equal to zero when the power is odd and higher than one and all but the first Mod function are equal to...
  8. M

    Fermat's Last Theorem FLT

    Are there any resources which describe FLT in a very tangible way which will motivate students to be interested in this subject?
  9. P

    Fermat Little Theorem "maximal" extension

    I remember finding a paper that presented a "maximal" extension to Fermat's Little Theorem. I got as far as the case where $n$ is a product of distinct primes $p_i$ and if $l = lcm \{p_i -1 \}$ then: $$\forall x: \ x^{l+1} = x \ (mod \ n)$$ Does anyone know of an extension to this, where...
  10. L

    Fermat's Last for >3 terms, n>0

    Fermat's Last Theorem states that no three positive integers a, b, and c satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Is there a solution for four or more such terms with an integer n>0?
  11. O

    Fermat Theorem Question

    In Fermat's Last Theorem ... do the numbers to the left of the equal sign have to be different? I'm looking for close solutions ... and have (after several years)found two systems which (I think) predicts them ... possibly to infinity. For example 4^3 + 4^3 -3 = 5^3 or 64 + 64 - 3 = 125 This...
  12. L

    Fermat's last with inverse powers

    Does a^(x^-1) + b^(x^-1) = c^(x^-1) hold true for any integers {a, b, c, x}>1 where "a" does not equal "b"?
  13. V

    Fermat's theorem. Proof by 2 operations

    Fermat's theorem. Proof by 2 operations The essence of the contradiction. The hypothetical Fermat's equality is contradictory between the second digits of the factors of the number $А$. All calculations are done with numbers in base n, a prime number greater than 2. The notations that...
  14. C

    Connection between Fermat's and Roth's theorem

    There is a Connection between Fermat's the Last and Roth's theorem that opens another (infinite) branch in Complcate Numbers investigation... :eek: I discover it writing the complete / general (as possible) definition for a Complicate Number... Very interesting, but will be a neverendingstory...
  15. C

    Fermat The last and the Trinomial Development

    What Fermat the Last has to do with the Trinomial Development ? Here the answer in the easy case $n=2$ Knowing that: \[P^2= \sum_{X=1}^{P} (2X-1)\] We can rewrite FLT for $n=2$ as: \[ \sum_{X=1}^{C} (2X-1) = \sum_{X=1}^{A} (2X-1) + \sum_{X=1}^{B} (2X-1) \] Now just applying the Sum...
  16. M

    Simple(st) Proof of Fermat's Last Theorem.

    \begin{align*} a^2+b^2&=c^2\\ c^2-a^2&=b^2\\ c^2-a^2&=(c-a)(c+a)\\ b^2&=(c-a)(c+a) \end{align*} This is possible iff there exists integers $k$, $x_1$, and $x_2$ such that $c-a=kx_1^2$ and $c-a=kx_2^2$ to give} $$b^2=k^2x_1^2x_2^2$$ For $n>2$, \begin{align*} a^n+b^n&=c^n\\ c^n-a^n&=b^n\\...
  17. R

    Fermat was correct... he had a truly marvelous simple proof of his last theorem.

    Fermat was correct,,, he had a truly marvelous proof of his last theorem. However, he has provided his proof only for n=4 which itself was significant. He may have mistaken about his trivial proof for odd primes. But here we showed that truly marvelous proof for odd primes...
  18. C

    Fermat's rosebud

    I hope this will be the correct end of Fermat the last: In case $n>2$ the First Derivate is a Curve So for any Symmetric condition we fix on $Y$ C^n = 2A^n+\Delta & C^n = 2B^n-\Delta So not just the Fermat's one I've shown in my previous post with: \Delta=\sum_{A+1}^{B}(X^n-(X-1)^n))...
  19. L

    Fermat's last theorem

    FERMAT’S LAST THEOREM an + bn = cn No three positive integers a, b and c satisfy the equation for value of n greater than 2 21power3 + 35power3 = 44power3 9261 +...
  20. L

    Generalized Fermat equation, N+1 terms, power N

    (a1)^N+(a2)^N+...+(aN)^N=(a0)^N Is there at least one solution to this equation for every natural, nonzero N?