fermat's theorem Definition and 14 Threads

  1. M

    Why Can We Take Limits of Both Sides? [Answered]

    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!
  2. M

    Find the units digit of ## 3^{100} ## by the use of Fermat's theorem

    Consider modulo ## 10 ##. Then ## 10=5\cdot 2 ##. Applying the Fermat's theorem produces: ## 3^{4}\equiv 1\pmod {5} ##. This means ## (3^{4})^{25}=3^{100}\equiv 1\pmod {5} ##. Observe that ## 3\equiv 1\pmod {2}\implies 3^{100}\equiv 1\pmod {2} ##. Now we have ## 5\mid (3^{100}-1) ## and ##...
  3. F

    MHB Fermat's Theorem: Did Fermat Have a Proof?

    In your opinion did Fermat have a proof for his theorem?
  4. I

    MHB Fermat's theorem (stationary points) of higher dimensions

    [FONT=Georgia]Look at this page and the Proof part, Fermat's theorem (stationary points) - Wikipedia, the free encyclopedia [FONT=Georgia]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?
  5. B

    How Does the Secant Line Relate to Fermat's Theorem?

    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...
    • Bipolarity
    • Thread
    • fermat's theorem Line Secant Theorem
    • Replies: 1
    • Forum: Calculus
  6. B

    Simple proof of Fermat's theorem?

    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 =/...
  7. E

    Fermat's theorem applied to multivariate functions

    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.
    • elementbrdr
    • Thread
    • Applied fermat's theorem Functions Multivariate Theorem
    • Replies: 11
    • Forum: Calculus
  8. dkotschessaa

    Is the work on Fermat's Theorem really done?

    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...
  9. W

    Could someone explain to me Fermat's 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...
  10. E

    Fermat's Theorem: Proven by Euler and By Me?

    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...
  11. A

    Extension of Fermat's theorem?

    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...
    • ACG
    • Thread
    • Extension fermat's theorem Theorem
    • Replies: 7
    • Forum: General Math
  12. G

    What Makes a Vertex Dynamic in Shape Diversity?

    Edit in new post. Or Bumping with the edited change.
  13. U

    Fermat's Theorem: A Math Problem and the Smart Boy Who Proved It Wrong

    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.
  14. T

    Fermat's theorem disproved (not really)

    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 . It is a funny read if you have the time.