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• Power of a Point Theorem Introductory Problem 1
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 1]]
  61 bytes (8 words) - 09:19, 1 July 2006
• Power of a Point Theorem Introductory Problem 2
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 2]]
  61 bytes (8 words) - 09:25, 1 July 2006
• Power of a Point Theorem Introductory Problem 3
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 3]]
  61 bytes (8 words) - 09:27, 1 July 2006
• Power of a Point Theorem Introductory Problem 4
  #REDIRECT [[Power of a Point Theorem/Introductory Problem 4]]
  61 bytes (8 words) - 09:27, 1 July 2006
• Power set
  The '''power set''' of a given [[set]] <math>S</math> is the set <math>\mathcal{P}(S)</m Similarly, for any [[finite]] set with <math>n</math> elements, the power set has <math>2^n</math> elements.
  4 KB (757 words) - 11:44, 8 March 2018
• Perfect power
  ...math> is a perfect <math>2</math>nd, <math>3</math>rd and <math>6</math>th power. ...h>st power" is a meaningless property: every integer is a <math>1</math>st power of itself.
  870 bytes (148 words) - 16:52, 18 August 2013
• Power's of 2 in pascal's triangle
  2 KB (341 words) - 16:57, 16 June 2019
• Power
  ...oosely defined as the speed something can do [[work]]. The [[SI]] unit for power is the [[Watt]]. ...d of [[time]]. It is also the [[derivative]] of work. If <math>P</math> is power, <math>W</math> is work, and <math>t</math> is time, then:
  467 bytes (77 words) - 23:26, 2 March 2008
• Power mean inequality
  #REDIRECT [[Power Mean Inequality]]
  35 bytes (4 words) - 21:24, 20 December 2007
• Besot Power Series
  Besot's Power Series Theorem states that
  725 bytes (145 words) - 15:51, 17 February 2016
• Power of a Point
  #REDIRECT [[Power of a Point Theorem]]
  38 bytes (6 words) - 16:53, 15 April 2019
• Root-mean power
  ...Geometric Mean: 0 (theoretical, can't be solved using radicals), Harmonic Mean: -1
  539 bytes (92 words) - 01:01, 2 November 2023
• 2023 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2023/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2023/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 21:17, 20 January 2024
• 2022 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2022/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2022/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 21:30, 20 January 2024
• 2021 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2021/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2021/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 21:39, 20 January 2024
• 2020 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2020/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2020/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:28, 22 January 2024
• 2019 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2019/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2019/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:34, 22 January 2024
• 2018 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2018/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2018/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:20, 29 January 2024
• 2014 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2014/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2014/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:25, 29 January 2024
• 2013 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2013/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2013/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:20, 5 February 2024

Page text matches

• San Diego ARML
  ** Power: 33 ** Power: 17
  2 KB (378 words) - 16:34, 5 January 2010
• Fermat's Little Theorem
  .../math> as a product of cyclic groups of prime order where the set of prime power orders is unique. We can do this because if any two prime powers are not c
  16 KB (2,658 words) - 16:02, 8 May 2024
• Harmonic mean
  ...d of mean (like [[arithmetic mean]] and [[geometric mean]]). The harmonic mean of a [[set]] of <math>n</math> [[positive]] [[real number]]s <math> x_1, x_ ...to avoid division by zero. For instance, if we tried to take the harmonic mean of the set <math>\{-2, 3, 6\}</math> we would be trying to calculate <math>
  1 KB (196 words) - 00:49, 6 January 2021
• Rearrangement Inequality
  ...e to be [[positive]] or negative, unlike the [[Power mean inequality|power-mean]] family of inequalities. *[[Power Mean Inequality]]
  5 KB (804 words) - 13:54, 26 January 2023
• Divisibility rules
  .../math> if and only if the last <math>n</math> digits are divisible by that power of 5. ...zeros that should be at the end of a number for it to be divisible by that power of 10.
  8 KB (1,298 words) - 15:07, 23 May 2024
• Induction
  ...s an emphasis on proof. Induction problems can be found anywhere from the Power Round of the [[American Regions Math League | ARML]] up through the [[Unite ...number of odd binomial coefficients in any row of the Pascal triangle is a power of 2. (1956 Putnam Competition)
  5 KB (768 words) - 20:45, 1 September 2022
• Jensen's Inequality
  ...t examples of Jensen's inequality is the [[quadratic mean]] - [[arithmetic mean]] inequality. Taking <math>F(x)=x^2</math>, which is convex (because <math> Similarly, [[arithmetic mean]]-[[geometric mean]] inequality ([[AM-GM]]) can be obtained from Jensen's inequality by consid
  3 KB (623 words) - 13:10, 20 February 2024
• Generating function
  ...ath>, give the terms of a [[sequence]] which is of interest. Therefore the power series (i.e. the generating function) is <math>c_0 + c_1 x + c_2 x^2 + \cdo ...the result is uninteresting (both the generating function and the desired power series are just <math>1</math>).
  4 KB (659 words) - 12:54, 7 March 2022
• Binomial Theorem
  Since <math>e^{a+b} = e^ae^b</math>, and power series for the same function are termwise equal, the series at <math>x = a
  5 KB (935 words) - 13:11, 20 February 2024
• Prime number
  ...prime, ''n'' must not have any odd divisor larger than 1 and so must be a power of 2. Therefore all Fermat primes have the form <math>2^{2^n}+1</math>. [[
  6 KB (985 words) - 12:38, 25 February 2024
• Circle
  *Lengths of chords can be calculated by using the [[Power of a point]] theorem. * [[Power of a point]]
  9 KB (1,581 words) - 18:59, 9 May 2024
• Divisor
  ...s often useful to know that this expression grows slower than any positive power of <math>{n}</math> as <math>n\to\infty</math>.
  1 KB (274 words) - 19:50, 29 August 2023
• Base numbers
  ...r in 2746 is actually just a placeholder which shows how many of a certain power of 10 there are. The first digit to the left of the decimal place (recall
  4 KB (547 words) - 17:23, 30 December 2020
• National Online Math League
  ...ilar to that used by the [[American Regions Math League]]: a Team test, a Power question, and several Relays. However, one match used an experimental form
  3 KB (452 words) - 11:21, 25 June 2006
• Least common multiple
  ...me number]] which divides any of them, take the largest [[exponentiation | power]] with which it appears, and multiply the results together. For example, t ...; the largest power of 3 that appears is <math>3^1</math>; and the largest power of 5 that appears is <math>5^1</math>. Therefore the LCM, <math>LCM(8, 12,
  2 KB (383 words) - 10:49, 4 September 2022
• Pi
  ...> is Liouvillian, then so is any rational multiple of any positive integer power of <math>x</math> (this is a simple exercise we leave to the reader), so, i Since the largest possible power of a given [[prime number|prime]] <math>p\le n</math> that can divide one o
  8 KB (1,469 words) - 21:11, 16 September 2022
• Logarithm
  ...ogs also allow (with repetition) to turn left to right exponentiation into power towers (especially useful for tetration (exponentiation repetition with the ...to the usual logarithm by the fact that if <math>b</math> isn't an integer power of <math>a</math> then <math>\lceil \log_a(m)\rceil</math> is a lower bound
  4 KB (680 words) - 12:54, 16 October 2023
• Utah ARML
  ...d in the B division, but was mislisted in the A division. However, on the Power Question, the Utah team got the 9th best score in the nation, which would h
  565 bytes (88 words) - 12:29, 11 December 2007
• Vocabulary and spelling competitions
  * [[Reader's Digest National Word Power Challenge | Word Power Challenge]] The premier vocabulary competition, for 6-8th grades. Over 3 mi
  786 bytes (99 words) - 17:53, 22 June 2006
• Vocabulary competitions
  * [[Reader's Digest National Word Power Challenge | Word Power Challenge]] The premier vocabulary competition, for 6-8th grades. Over 3 mi
  392 bytes (50 words) - 02:36, 29 November 2018

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