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• Callebaut's Inequality
  ...th>(\frac xy-1)</math>th, <math>\frac xy</math>th, <math>\frac xy</math>th power, we get
  1 KB (236 words) - 17:30, 4 December 2010
• Python reference
  This function returned e raised to the second power.
  28 KB (4,762 words) - 21:20, 12 June 2023
• '''2.''' ''Power-mean inequality'': For <math>a_1, a_2,\cdots,a_n>0</math> and <math>k\geq l,</ma
  1 KB (197 words) - 12:12, 29 October 2016
• 2010 AMC 10B Problems/Problem 22
  ...hite bag: <math>2^{7-r}</math>. Because we aren't fixing one for blue, the power is <math>7-r</math> instead of <math>7-r-1</math>
  4 KB (750 words) - 22:59, 18 January 2024
• Powers of 2
  A power of 2 means a number of the form <math>2^n</math>, in which <math>n</math> i
  930 bytes (37 words) - 12:17, 20 December 2018
• 2011 AMC 12A Problems
  ...9 hours after leaving dock <math>A.</math> How many hours did it take the power boat to go from <math>A</math> to <math>B?</math>
  13 KB (1,994 words) - 13:52, 3 July 2021
• 2011 AMC 12A Problems/Problem 12
  ...9 hours after leaving dock <math>A.</math> How many hours did it take the power boat to go from <math>A</math> to <math>B</math>? ...nce that is how the problem is given to us. Think of the blue arrow as the power boat and the red arrow as the raft in the following three diagrams, which r
  5 KB (928 words) - 23:01, 14 April 2022
• 2011 AMC 12A Problems/Problem 19
  ...\lfloor\log_{2}(N-1)\rfloor} - N</math> is the difference between the next power of 2 above <math> 2^{\lfloor\log_{2}(N-1)\rfloor}</math> and <math>N</math> ...8</math> will not work because two powers of two will never sum to another power of <math>2</math> (unless they are equal, which is a contradiction to the q
  4 KB (563 words) - 11:12, 3 December 2023
• 2011 AMC 10B Problems/Problem 23
  In all of the other terms, the power of <math>10</math> is greater than <math>2</math> and so is equivalent to < ...e numbers from 1 to 11 (since the hundreds digit increases by 1 with every power of 11 that comes after) to get the hundreds digit of <math>11^{11}</math>.
  9 KB (1,288 words) - 20:47, 13 June 2024
• Descartes' Circle Formula
  (based on wording of ARML 2010 Power)
  2 KB (288 words) - 21:00, 24 December 2017
• 2011 AIME I Problems/Problem 7
  ..._{2010}}</math> equal to <math>1-\left(\frac{1}{m}\right)^x</math> for any power of <math>x</math>. Consider <math>m=2</math>. We can achieve a sum of <math .... Since there are <math>m + j(m-1)</math> terms after the <math>j</math>th power, we will only hit exactly 2011 terms if <math>m-1</math> is a factor of 201
  11 KB (1,760 words) - 01:16, 14 June 2024
• Deficient number
  Prove that all [[perfect power|powers]] of [[prime number|prime numbers]] are deficient.
  719 bytes (88 words) - 12:39, 9 February 2018
• 2011 AIME II Problems/Problem 10
  ...s than 7, and similarly for <math>PB</math> and <math>PA</math>). Then, by Power of a Point on P with respect to the circle with center <math>O</math>, we h
  11 KB (1,720 words) - 03:12, 18 December 2023
• 2011 USAMO Problems
  ...remainder upon dividing <math>2^{2^n}</math> by <math>2^n - 1</math> is a power of 4. Either prove the assertion or find (with proof) a counterexample.
  3 KB (484 words) - 12:26, 17 April 2016
• 2011 USAJMO Problems
  ...remainder upon dividing <math>2^{2^n}</math> by <math>2^n - 1</math> is a power of 4. Either prove the assertion or find (with proof) a counterexample.
  3 KB (447 words) - 16:40, 5 August 2023
• 2011 USAJMO Problems/Problem 5
  == The Power of Angle Chasing ==
  4 KB (717 words) - 17:00, 14 April 2024
• 2011 USAMO Problems/Problem 4
  ...he remainder upon dividing <math>2^{2^n}</math> by <math>2^n-1</math> is a power of 4. Either prove the assertion or find (with proof) a counter-example. ...h> is an odd power of 2 for some <math>\textstyle n</math>, and thus not a power of 4.
  3 KB (494 words) - 15:41, 25 April 2021
• 2000 AMC 8 Problems/Problem 9
  The only <math>3</math>-digit power of <math>2</math> beginning with <math>2</math> is <math>256</math>, so the
  1 KB (153 words) - 18:34, 28 March 2023
• 2003 AMC 10B Problems/Problem 14
  <math>405</math> is not a perfect power, so the smallest possible value of <math>a+b</math> is <math>405+2=\boxed{\
  682 bytes (96 words) - 16:22, 23 June 2021
• 1998 AJHSME Problems/Problem 16
  The power of <math>3</math> that <math>30</math> is closest to is <math>27=3^3</math>
  1 KB (206 words) - 17:52, 17 April 2021

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