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- ==Problem== ...ion again, we have <math>\lambda(100)=20</math>, so <math>N=3^{27}\equiv 3^7\pmod{100}\equiv 87\pmod{100}</math>. Therefore <math>n=87</math>, and so we1 KB (127 words) - 23:15, 4 January 2010
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- ...ake. Sometimes, the administrator may ask other people to sign up to write problems for the contest. ...AMC]] competition. There is no guarantee that community members will make Mock AMCs in any given year, but there probably will be one.51 KB (6,175 words) - 20:41, 27 November 2024
- The '''Mock AIME 1 2005-2006''' was written by [[Art of Problem Solving]] community member paladin8. * [[Mock AIME 1 2005-2006/Answer Key|Answer Key]]1 KB (135 words) - 16:41, 21 January 2017
- The '''Mock AIME 1 2006-2007''' was written by [[Art of Problem Solving]] community member Altheman. * [[Mock AIME 1 2006-2007/Problems|Entire Exam]]1 KB (155 words) - 15:06, 3 April 2012
- The '''Mock AIME 2 2006-2007''' was written by [[Art of Problem Solving]] community member 4everwise. * [[Mock AIME 2 2006-2007 Problems|Entire Exam]]1 KB (145 words) - 09:55, 4 April 2012
- Let <math>\triangle ABC</math> have <math>BC=\sqrt{7}</math>, <math>CA=1</math>, and <math>AB=3</math>. If <math>\angle A=\frac{ ...o <math>3^{2000}\equiv 1 \pmod{1000}</math> and so <math>3^{2007} \equiv 3^7 \equiv 2187 \equiv 187 \pmod{1000}</math>963 bytes (135 words) - 14:53, 3 April 2012
- ...= (a + b) - b = 12</math>, so our three vertices are <math>(-7, 49), (-2, 4)</math> and <math>(12, 144)</math>. *[[Mock AIME 1 2006-2007 Problems/Problem 3 | Previous Problem]]1 KB (244 words) - 14:21, 5 November 2012
- ==Problem== ...h>P_{1}: y=x^{2}+\frac{101}{100}</math> and <math>P_{2}: x=y^{2}+\frac{45}{4}</math> be two [[parabola]]s in the [[Cartesian plane]]. Let <math>\mathcal3 KB (460 words) - 14:52, 3 April 2012
- ==Problem== ...>, <math>BC</math>, and <math>CA</math> have lengths <math>3</math>, <math>4</math>, and <math>5</math>, respectively. Let the incircle, circle <math>I<1 KB (236 words) - 22:58, 24 April 2013
- ==Problem== We will solve this problem by constructing a [[recursion]] satisfied by <math>\mathcal{S}_n</math>.2 KB (424 words) - 14:51, 3 April 2012
- ==Problem== ...7</math>, <math>d_{5}=13</math>, and <math>d_{6}=-16</math>, find <math>d_{7}</math>.3 KB (568 words) - 14:50, 3 April 2012
- ==Problem 1== [[Mock AIME 1 2006-2007 Problems/Problem 1|Solution]]8 KB (1,355 words) - 13:54, 21 August 2020
- == Problem == ...th> and <math>x_{n+3} = x_{n+2}(x_{n+1}+x_n)</math> for <math>n = 1, 2, 3, 4</math>. Find the last three [[digit]]s of <math>x_7</math>.3 KB (470 words) - 23:33, 9 August 2019
- ==Problem== ...ion again, we have <math>\lambda(100)=20</math>, so <math>N=3^{27}\equiv 3^7\pmod{100}\equiv 87\pmod{100}</math>. Therefore <math>n=87</math>, and so we1 KB (127 words) - 23:15, 4 January 2010
- ==Problem== .../math>, by [[Euler's Totient Theorem]] <math>2^{20 \cdot 100 + 7} \equiv 2^7 \equiv 3 \pmod{125}</math>. Combining, we have <math>2^{2007} \equiv 128 \p4 KB (595 words) - 11:14, 25 November 2023
- ==Problem== ...math>, we see that <math>f(1)=0, f(2)=0, f(3)=0, f(4)=1, f(5)=1, f(6)=2, f(7)=2,992 bytes (156 words) - 19:34, 27 September 2019
- == Problem == So all of the prime numbers less than <math>50</math> are <math>2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,</math> and <math>47</math>. So we2 KB (209 words) - 11:43, 10 August 2019
- In the context of problem-solving, the characteristic polynomial is often used to find closed forms f ...can be solved for each constant. Refer to the [[#Introductory|introductory problems]] below to see an example of how to do this. In particular, for the Fibonac19 KB (3,412 words) - 13:57, 21 September 2022
- ...contains the full set of test problems. The rest contain each individual problem and its solution. The Mock AIME 5 2006-2007 was written by Art of Problem Solving community member Altheman.1 KB (172 words) - 13:37, 3 July 2012
- ...contains the full set of test problems. The rest contain each individual problem and its solution. The Mock AIME 6 2006-2007 was written by Art of Problem Solving community member paladin8.1 KB (172 words) - 13:39, 3 July 2012
- ...contains the full set of test problems. The rest contain each individual problem and its solution. The Mock AIME 7 2006-2007 was written by Art of Problem Solving community member Altheman.1 KB (160 words) - 13:44, 3 July 2012