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• 2012 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2012/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2012/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:25, 5 February 2024
• 2011 Power
  * [https://www.stanfordmathtournament.com/pdfs/smt2011/power-problems.pdf/ Problems] * [https://www.stanfordmathtournament.com/pdfs/smt2011/power-solutions.pdf/ Solutions]
  171 bytes (18 words) - 22:29, 5 February 2024
• Power of a point theorem
  6 KB (1,010 words) - 02:38, 7 May 2024

Page text matches

• Mathew Crawford
  * Headed up the grading of the Power Round for the Georgia ARML site (2010)
  2 KB (360 words) - 02:20, 2 December 2010
• Fermat's Last Theorem
  ...to be the sum of two fourth powers, or in general for any number that is a power greater than the second to be the sum of two like powers. ''I have discover
  3 KB (453 words) - 11:13, 9 June 2023
• Diophantine equation
  Note that every square, and therefore every fourth power, is either <math>1</math> or <math>0\mod 4</math>. The proof of this is fai
  9 KB (1,434 words) - 13:10, 20 February 2024
• Pascal's triangle
  ...s Theorem, which states that given a prime p and integers m,n, the highest power of p dividing <math>\binom{m}{n}</math> is the number of carries in adding
  5 KB (838 words) - 17:20, 3 January 2023
• Newton's Sums
  ...cient way of finding the sums of [[root]]s of a [[polynomial]] raised to a power. They can also be used to derive several [[factoring]] [[identity|identiti
  4 KB (690 words) - 13:11, 20 February 2024
• Exponentiation
  ...ten in the form <math>a^b</math>, where <math>b</math> is the exponent (or power) and <math>a</math> is the [[base]]. ...times. The base is 3 (what is repeatedly multiplied) and the exponent (or power) is 5 (the number of times to repeat multiplication).
  5 KB (803 words) - 16:25, 10 August 2020
• Root-Mean Square-Arithmetic Mean-Geometric Mean-Harmonic mean Inequality
  ...root-mean power]], [[arithmetic mean]], [[geometric mean]], and [[harmonic mean]] of a set of [[positive]] [[real number]]s <math>x_1,\ldots,x_n</math> th ...,~~0<n_2<1,~~-1<n_3<0,~~n_4<-1</math>, and <math>n</math> is the root mean power.
  5 KB (912 words) - 20:06, 14 March 2023
• Power of a Point Theorem
  The '''Power of a Point Theorem''' is a relationship that holds between the lengths of t ...ugh <math>P</math> that intersects the circle. This constant is called the power of point <math>P</math>. For example, in the figure below
  5 KB (828 words) - 23:10, 25 June 2024
• Alt front page
  ...><br>Cacti is a complete network graphing solution designed to harness the power of RRDTool's data storage and graphing functionality. Cacti provides a fast
  2 KB (329 words) - 17:25, 8 June 2008
• Rational approximation of famous numbers
  ..., that <math>x</math> is not a [[Liouvillian number]], i.e., that for some power <math>M<+\infty</math>, the [[inequality]] <math>\left|x-\frac pq\right|\ge Since the largest possible power of a given prime <math>p\le n</math> that can divide one of the numbers <ma
  8 KB (1,431 words) - 13:48, 26 January 2008
• Reader's Digest National Word Power Challenge
  The '''Reader's Digest National Word Power Challenge''' is the first nationwide vocabulary competition for middle scho ...dependencies thereof, who have not previously won a scholarship from Word Power, can participate.
  2 KB (293 words) - 21:13, 20 March 2008
• Bertrand's Postulate
  Note that the power with which a prime <math>p</math> satisfying <math>\frac{2n}3<p\le n</math>
  2 KB (309 words) - 21:43, 11 January 2010
• Perfect square
  * [[Perfect power]]
  954 bytes (155 words) - 01:14, 29 November 2023
• Uncountable
  ...th>|S|<|\mathcal{P}(S)|</math>, where <math>\mathcal{P}(S)</math> is the [[power set]] of <math>S</math>. First, we note that the [[Cantor set]] <math>\math
  2 KB (403 words) - 20:53, 13 October 2019
• Subset
  The set of all subsets of a given set <math>S</math> is called the [[power set]] of <math>S</math> and is denoted <math>\mathcal{P}(S)</math> or <math
  1 KB (217 words) - 09:32, 13 August 2011
• 2006 AIME I Problems
  ...tive integer <math> x, </math> let <math> g(x) </math> denote the greatest power of 2 that divides <math> x. </math> For example, <math> g(20)=4 </math> and
  7 KB (1,173 words) - 03:31, 4 January 2023
• 2006 AIME I Problems/Problem 13
  ...ve integer]] <math> x </math>, let <math> g(x) </math> denote the greatest power of 2 that [[divisor | divides]] <math> x. </math> For example, <math> g(20) ...ath> that divides <math>n+1</math>. Thus by the above formula, the highest power of <math>2</math> that divides <math>S_n</math> is <math>2^{k+n-1}</math>.
  10 KB (1,702 words) - 00:45, 16 November 2023
• 2006 AIME I Problems/Problem 9
  The product of <math>a^2</math> and <math>r^{11}</math> is a power of 2. Since both numbers have to be integers, this means that <math>a</mat ...ly not possible. Thus the only restriction r has is that it must be an odd power of 2, so <math>2^{1}</math>, <math>2^{3}</math>, <math>2^{5}</math> .... al
  4 KB (651 words) - 18:27, 22 May 2021
• 2006 AIME I Problems/Problem 4
  A number in decimal notation ends in a zero for each power of ten which divides it. Thus, we need to count both the number of 5s and ...h> - every <math>n!</math> term for <math>n\geq25</math> has an additional power of <math>5</math> dividing it, for <math>76</math> extra; every n! for <mat
  2 KB (278 words) - 08:33, 4 November 2022
• 2006 AMC 12B Problems/Problem 20
  ...eq 0</math> is the lowest value such that <math>4x</math> becomes a higher power of 10.
  3 KB (485 words) - 14:09, 21 May 2021

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