fermat

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...

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.

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...

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

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...

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...

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...

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

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...

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?

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...

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"?

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...

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...

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...

\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\\...

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...

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))...

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 +...

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