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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

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• 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
• Complex number
  *[[2007 AMC 12A Problems/Problem 18]] *[[1984 AIME Problems/Problem 8|1984 AIME Problem 8]]
  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. ...d the product <math> n_1\cdot n_2</math>. ([[2005 AIME II Problems/Problem 13|Source]])
  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
• 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 II Problems/Problem 15
  == Problem == label("$\ell$",(13,l(13)),SE,fontsize(9));
  12 KB (2,001 words) - 20:26, 23 July 2024
• 2005 AIME II Problems/Problem 14
  == Problem == In [[triangle]] <math> ABC, AB=13, BC=15, </math> and <math>CA = 14. </math> Point <math> D </math> is on <ma
  14 KB (2,340 words) - 16:38, 21 August 2024
• 2004 AIME II Problems
  {{AIME Problems|year=2004|n=II}} == Problem 1 ==
  9 KB (1,410 words) - 05:05, 20 February 2019
• Mock AIME 5 Pre 2005 Problems
  == Problem 1 == [[Mock AIME 5 Pre 2005 Problems/Problem 1|Solution]]
  6 KB (909 words) - 07:27, 12 October 2022
• 2009 AIME II Problems/Problem 7
  == Problem == ...</math> will yield an answer <math>>999</math>, which cannot happen on the AIME.) Once you calculate the value of <math>4010</math>, and divide by <math>10
  8 KB (1,312 words) - 16:23, 30 March 2024

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