What is fermat's theorem: Definition and 16 Discussions
The works of the 17th-century mathematician Pierre de Fermat engendered many theorems. Fermat's theorem may refer to one of the following theorems:
Fermat's Last Theorem, about integer solutions to an + bn = cn
Fermat's little theorem, a property of prime numbers
Fermat's theorem on sums of two squares, about primes expressible as a sum of squares
Fermat's theorem (stationary points), about local maxima and minima of differentiable functions
Fermat's principle, about the path taken by a ray of light
Fermat polygonal number theorem, about expressing integers as a sum of polygonal numbers
Fermat's right triangle theorem, about squares not being expressible as the difference of two fourth powers
For this,
Does someone please know why we are allowed to take limits of both side [boxed in orange]?
Also for the thing boxed in pink, could we not divide by -h if ##h > 0##?
Many thanks!
Hello,
I've been using Caratheodory's Lemma to prove the Inverse Function Theorem and Fermat's Theorem. I have managed to prove both of them, I would just like someone to look over my proof and tell me if I'm missing anything (i.e. should I clarify any parts of my proof). So here goes:
Inverse...
Look at this page and the Proof part,
Fermat's theorem (stationary points) - Wikipedia, the free encyclopedia
How to change the proof 2 into a proof of higher dimensions or can you give a proof of Fermat's theorem of higher dimensions?
I'm trying to understand something in Fermat's Theorem. I can't really phrase it in words, but I will write what my textbook says.
Apparently if
\lim_{x→c}\frac{f(x)-f(c)}{x-c} > 0
then there exists an open interval (a,b) containing c such that
\frac{f(x)-f(c)}{x-c} > 0 for all...
Can someone point out the error in the following "proof":
Prove a^n + b^n =/ c^n for n>2, a,b,c>1 (=/ means not equal to)
Let b=xa where x>1 and is from the set of real numbers generated by fractions, such that b is an integer
so:
a^n + (xa)^n =/ c^n
Expanding
a^n + x^n.a^n =/...
Fermat's theorem provides that, if a function f(x) has a local max or min at a, and if f'(a) exists, then f'(a)=0. I was wondering whether a similar theory exists for a function f(x,y) or f(x,y,z) etc.
(1). Prove the following statements.
(a). When n = 2p, where p is an odd prime, then a^(n-1) = a (mod n) for any integer a.
(b). For n = 195 = 3 * 5 *13, we have a^(n-2) = a (mod n) for any integer a
If I am correct Fermat's Theorem comes into play.
a)n=2p
a^(2p-1)
a^(2p)*(1/a)...
I'm still relatively new to mathematics, in the sense of studying it with any degree of seriousness, so I have a question related to the general field of mathematics and a little bit on it's history.
I haven't read Simon Singh's book yet,but a I understand the story on Fermat's Last Theorem...
I DO NOT like this least time hocus pocus. I prefer the idea of causality. I just CANNOT stomach this idea. Here are my arguments (italicized text) almost verbatim from my notes against what I read (in bold). Someone please explain to me the whys and hows.
Arguments against Fermat:
"Given...
I'm talking about neither his "last theorem" nor his "little theorem", but another one. He suggested that
x^2+2=y^3 can only have one solution (if we're dealing in natural numbers), which was (5,3). Euler reproved the theorem since, like so many others of his, the proof was lost. I can't...
Hi! I assume you all know Fermat's last theorem. Well, has anyone considered the following extension to it? Assuming we're just using integers:
We know that x1^n + x2^n = y^n has no solution for n > 2. However, what about this?
For which values of k does x1^n+x2^n+...+xk^n = z^n...
from: http://www.math.utah.edu/~cherk/puzzles.html
I am stumped, I noticed the pattern in the digits of the numbers, but I do not see how I can link that to the possibility of forming such a statement with those numbers when n is greater than 2.
I read a book on Fermat's last theorem (a^n + b^n = c^n has no integer solutions for n > 2) last summer and I found this while trying to find the actual proof: http://home.mindspring.com/~jbshand/ferm.html [Broken]. It is a funny read if you have the time.