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• 2005 AIME II Problems/Problem 13
  == Problem == ...olutions so <math>P(x)</math> is at least quadratic. Let us first try this problem out as if <math>P(x)</math> is a quadratic polynomial. Thus <math>P(n)-(n+3
  4 KB (642 words) - 02:14, 1 June 2024
• 2005 AIME I Problems/Problem 13
  == Problem == ...assign to <math>(0,1,0)</math>. (We will see how this correlates with the problem.) Then define for each lattice point <math>(i,j)</math> its triplet thus:
  5 KB (897 words) - 00:21, 29 July 2022
• Mock AIME 3 Pre 2005 Problems/Problem 13
  ==Problem== <math>13.</math> Let <math>S</math> denote the value of the sum
  3 KB (502 words) - 14:53, 19 July 2020
• Mock AIME 1 Pre 2005 Problems/Problem 13
  ==Problem==
  1 KB (178 words) - 14:22, 26 March 2011
• Mock AIME 5 2005-2006 Problems/Problem 13
  == Problem == {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=12|num-a=14}}
  539 bytes (83 words) - 21:20, 8 October 2014

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• Simon's Favorite Factoring Trick
  ...nd make the equation factorable. It can be used to solve more than algebra problems, sometimes going into other topics such as number theory. == Fun Practice Problems ==
  4 KB (682 words) - 10:25, 18 February 2025
• Principle of Inclusion-Exclusion
  ...d only once. In particular, memorizing a formula for PIE is a bad idea for problem solving. ==== Problem ====
  9 KB (1,703 words) - 01:20, 7 December 2024
• Constructive counting
  This is a problem where constructive counting is not the simplest way to proceed. This next e ...proceed with the construction. If we were to go like before and break the problem down by each box, we'd get a fairly messy solution.
  13 KB (2,018 words) - 15:31, 10 January 2025
• Complex number
  == Problems == *[[2007 AMC 12A Problems/Problem 18]]
  5 KB (860 words) - 15:36, 10 December 2023
• Diophantine equation
  ...s for any given Diophantine equations. This is known as [[Hilbert's tenth problem]]. The answer, however, is no. == Problems ==
  9 KB (1,434 words) - 01:15, 4 July 2024
• 2004 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2004 AIME II Problems]]
  1 KB (135 words) - 12:24, 22 March 2011
• 2005 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME I Problems]]
  1 KB (154 words) - 12:30, 22 March 2011
• 2006 AIME I
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2006 AIME I Problems]]
  1 KB (135 words) - 12:31, 22 March 2011
• 2005 AIME II
  ...contains the full set of test problems. The rest contain each individual problem and its solution. * [[2005 AIME II Problems]]
  1 KB (135 words) - 12:30, 22 March 2011
• 2006 AIME I Problems
  {{AIME Problems|year=2006|n=I}} == Problem 1 ==
  7 KB (1,173 words) - 03:31, 4 January 2023
• Set
  ...describe sets should be used with extreme caution. One way to avoid this problem is as follows: given a property <math>P</math>, choose a known set <math>T< ==Problems==
  11 KB (2,019 words) - 17:20, 7 July 2024
• 2005 AIME II Problems/Problem 1
  == Problem == ...8, 9, and 10, which works, so <math>n - 3 = 10</math> and <math>n = \boxed{13}</math>.
  1 KB (239 words) - 11:54, 31 July 2023
• 2005 AIME II Problems/Problem 5
  == Problem == ...og_a b + 6\log_b a=5, 2 \leq a \leq 2005, </math> and <math> 2 \leq b \leq 2005. </math>
  3 KB (547 words) - 19:15, 4 April 2024
• 2005 AIME II Problems
  {{AIME Problems|year=2005|n=II}} == Problem 1 ==
  7 KB (1,119 words) - 21:12, 28 February 2020
• 2005 AIME II Problems/Problem 7
  == Problem == <cmath>(y^{14}+y^{12}+y^{10}+y^8+y^6+y^4+y^2+1)(y+1) = (y^{15}+y^{14}+y^{13}+y^{12}+y^{11}+y^{10}+y^9+y^8+y^7+y^6+y^5+y^4+y^3+y^2+y+1)=\frac{y^{16}-1}{
  2 KB (279 words) - 12:33, 27 October 2019
• 2005 AIME II Problems/Problem 12
  == Problem == ...^2</math> equal and solving for <math>x</math> (it is helpful to scale the problem down by a factor of 50 first), we get <math>x = 250\pm 50\sqrt{7}</math>. S
  13 KB (2,080 words) - 13:14, 23 July 2024
• 2005 AIME II Problems/Problem 10
  == Problem == ...<math>\frac{AF}2 = \frac s{\sqrt2}</math> and so it has volume <math>\frac 13 s^2 \cdot \frac s{\sqrt2} = \frac {s^3}{3\sqrt2}</math> and the whole octah
  3 KB (436 words) - 20:35, 13 August 2024
• 2005 AIME I Problems
  {{AIME Problems|year=2005|n=I}} == Problem 1 ==
  6 KB (983 words) - 05:06, 20 February 2019
• 2005 AIME I Problems/Problem 3
  == Problem == ...ss than <math>50</math>. There are fifteen of these (<math>2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43</math> and <math>47</math>) so there are <m
  2 KB (249 words) - 09:37, 23 January 2024
• 2005 AIME I Problems/Problem 4
  == Problem == ...th>. When <math>n = 28</math>, this product is <math>980</math>, and since AIME answers are nonnegative integers less than <math>1000</math>, we don't have
  8 KB (1,249 words) - 21:25, 20 November 2024

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