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  • == Algebraic Number Theory == ...}(\bar{\mathbb{Q}}/\mathbb{Q})</math>. Famous problems in algebraic number theory include the [[Birch and Swinnerton-Dyer Conjecture]] and [[Fermat's Last Th
    5 KB (849 words) - 15:14, 18 May 2021
  • All of the roots of unity lie on the [[unit circle]] in the complex plane. This can be seen by consideri * [[Number theory]]
    3 KB (558 words) - 20:36, 11 December 2011
  • ...iophantine equation is closely tied to [[modular arithmetic]] and [[number theory]]. Often, when a Diophantine equation has infinitely many solutions, [[para ...olutions to the diophantine equation correspond to [[lattice point]]s that lie on the line. For example, consider the equation <math>-3x+4y=4</math> or <
    9 KB (1,434 words) - 00:15, 4 July 2024
  • celebrated results in [[analytic number theory]]. Indeed, it is possibly the most famous major result in all of number theory, with
    11 KB (1,749 words) - 21:52, 10 January 2025
  • [[number theory]]. In particular, the [[Riemann Hypothesis]] is a conjecture <math>0 \le \Re(s) \le 1</math>. He conjectured that they all lie on the
    9 KB (1,547 words) - 02:04, 13 January 2021
  • The <math>231</math> cubes which are not visible must lie below exactly one layer of cubes. Thus, they form a rectangular solid whic [[Category:Intermediate Number Theory Problems]]
    2 KB (377 words) - 10:53, 10 March 2014
  • ...r primes) because <math>61 \cdot 2</math> and <math>61 \cdot 3</math> both lie in the interval <math>(100, 200)</math>. [[Category:Intermediate Number Theory Problems]]
    3 KB (399 words) - 10:53, 30 October 2024
  • ...we know that <math>1\leq a+b+c \leq 27</math> so only <math>7,16,25</math> lie in the interval [[Category:Intermediate Number Theory Problems]]
    3 KB (565 words) - 15:51, 1 October 2023
  • ...nates are both integers is called a lattice point. How many lattice points lie on the hyperbola <math>x^2 - y^2 = 2000^2</math>? [[Category:Intermediate Number Theory Problems]]
    1 KB (246 words) - 01:17, 18 December 2024
  • ...matic quantum field theory, it would have to be trivial (i.e. a free field theory). However, the quantum Yang-Mills theory (no quarks) with a non-abelian gauge group is an exception. It has a proper
    2 KB (363 words) - 14:31, 1 December 2015
  • ...rk is split into thirteen volumes. It covers not only geometry, but number theory and some algebra throughout various volumes. ...Theorem]]. The other volumes deal with a combination of algebra and number theory, though arguably volume 10 in fact lays the foundation for integral [[calcu
    12 KB (2,094 words) - 14:42, 1 December 2015
  • An '''ultrafilter''' is a [[set theory | set theoretic]] structure. ...n [[topology]]. They are also used to construct the [[hyperreals]], which lie at the foundations of [[non-standard analysis]].
    9 KB (1,685 words) - 19:28, 13 October 2019
  • ...urnside's Lemma''' is a [[combinatorics |combinatorial]] result in [[group theory]] that is useful for counting the [[orbit]]s of a [[set]] on which a [[grou ...attributed to Burnside because he quoted and proved it in his 1897 book ''Theory of groups of finite order'' without attribution, apparently because he thou
    5 KB (763 words) - 23:16, 18 November 2024
  • ...[[Poincaré Conjecture]], the [[Riemann Hypothesis]], and the [[Yang-Mills Theory]]. In 2003, the Poincaré Conjecture was proven by Russian mathematician [[ ...of P versus NP is an important problem in [[computability and complexity]] theory relating to whether decision problems (problems admitting a yes or no answe
    13 KB (1,969 words) - 16:57, 22 February 2024
  • and raising chickens as he does trying to map out a <math>\textit{Theory of Everything}</math>. Dr. Lisi often poses problems to the Kubik children ...nds of the ellipse where the ellipse intersects the line on which the bats lie. These two children are <math>40</math> feet apart. Five other children sta
    71 KB (11,749 words) - 11:39, 20 November 2024
  • By the SAS triangle simlarity theory, <math>\triangle APB \sim\triangle B'PA'</math>. That implies that <math>\a By the SAS triangle simlarity theory, <math>\triangle APB \sim\triangle A'PB'</math>. That implies that <math>\a
    5 KB (807 words) - 17:37, 25 June 2021
  • The theory of radical axis is a priceless geometric tool that can solve formidable geo ...a few challenging problems that are exemplary examples on how radical axis theory can be used and why it pertains to that situation. I hope after you read th
    12 KB (2,125 words) - 07:38, 23 May 2024
  • A triangle is called a parabolic triangle if its vertices lie on a [[Category:Olympiad Number Theory Problems]]
    6 KB (1,001 words) - 19:21, 11 September 2021
  • ==Solution (Group Theory)== ==Solution 2 (Function Theory)==
    2 KB (451 words) - 18:09, 1 May 2014
  • ...ng decimal of period <math>4</math>. In which interval does <math>n</math> lie? [[Category: Intermediate Number Theory Problems]]
    4 KB (565 words) - 23:33, 9 November 2024

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