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• Pythagorean Theorem
  Also note that one easy way to find Pythagorean triples is as follows. Choose any odd number <math ==== Solution 1 (Bash) ====
  6 KB (996 words) - 17:49, 22 March 2025
• Trivial Inequality
  ...lication is maximizing and minimizing [[quadratic]] functions. It gives an easy proof of the two-variable case of the [[AMGM | Arithmetic Mean-Geometric Me ..._2a_3+\cdots+a_{n-1}a_n+a_na_1</math>. [[Inequality_Introductory_Problem_2|Solution]]
  3 KB (583 words) - 21:20, 2 August 2024
• Completing the square
  ...that equation a [[perfect square]]. This makes solving a lot of equations easy. In fact, all [[quadratic equation]]s can be solved by completing the squa ==General Solution For A Quadratic by Completing the Square==
  2 KB (422 words) - 16:20, 5 March 2023
• Polynomial
  ...way (not counting re-arrangements of the terms of the product). It's very easy to find the roots of a polynomial in this form because the roots will be <m Given the coefficients of a polynomial, it is very easy to figure out the value of the polynomial on different inputs. In some cas
  6 KB (1,100 words) - 15:57, 30 August 2024
• 1959 IMO Problems/Problem 2
  == Solution 1 == This tells there that there is no solution for (b), since we must have <math>A^2 \ge 2</math>
  4 KB (612 words) - 00:19, 7 March 2025
• 1970 IMO Problems/Problem 6
  ==Solution== 1. The solution above contains an error (a typo?) and skips too many steps,
  6 KB (1,054 words) - 18:09, 11 December 2024
• Constructive counting
  '''Solution''': We can construct a four-digit by picking the first digit, then the seco '''Solution''': We can model this situation as a row of 7 boxes, like this: <cmath>\squ
  13 KB (2,018 words) - 15:31, 10 January 2025
• Complementary counting
  ...ler approach. A large hint that complementary counting may lead to a quick solution is the phrase "not" or "at least" within a problem statement. ...bility is not typically an intermediate step, but a framework upon which a solution is built.
  8 KB (1,192 words) - 17:20, 16 June 2023
• 2005 USAMO Problems/Problem 4
  == Solution 1 == For <math>0 \le x \le n</math>, it is easy to see that the number of stable tables is <math>(x+1)^2</math>.
  7 KB (1,276 words) - 20:51, 6 January 2024
• Diophantine equation
  Finding the solution or solutions to a Diophantine equation is closely tied to [[modular arithme ...(\frac{x_0}{d},\frac{y_0}{d},\frac{z_0}{d^2}\right)</math> would then be a solution less than <math>z_0</math>, which contradicts our assumption. Thus, this eq
  9 KB (1,434 words) - 01:15, 4 July 2024
• Alt front page
  ...anagement features out of the box. All of this is wrapped in an intuitive, easy to use interface that makes sense for LAN-sized installations up to complex
  2 KB (331 words) - 18:37, 21 February 2025
• 2006 AMC 12A Problems/Problem 25
  == Solution 1== ...and pattern-finding. We give a somewhat more general attack, based on the solution to the following problem:
  9 KB (1,409 words) - 03:59, 8 December 2024
• 2005 AIME I Problems/Problem 7
  == Solution == === Solution 1 ===
  5 KB (715 words) - 23:43, 24 March 2025
• 2005 AIME I Problems/Problem 11
  == Solution == ===Solution 1 ===
  4 KB (707 words) - 11:11, 16 September 2021
• 2005 AIME I Problems/Problem 13
  == Solution == === Solution 1 ===
  5 KB (897 words) - 00:21, 29 July 2022
• 2005 AIME II Problems/Problem 14
  == Solution 1== == Solution 2 (Similar Triangles)==
  14 KB (2,340 words) - 16:38, 21 August 2024
• 2004 AIME I Problems/Problem 15
  == Solution == === Solution 1 ===
  9 KB (1,491 words) - 01:23, 26 December 2022
• 2004 AIME I Problems/Problem 7
  === Solution 1 === === Solution 2 ===
  7 KB (1,099 words) - 13:41, 30 December 2024
• 2019 AIME I Problems/Problem 2
  ==Solution 1== ==Solution 2==
  5 KB (831 words) - 18:47, 29 January 2025
• 1983 AIME Problems/Problem 1
  == Solution 1 == ...>. If we now convert everything to a power of <math>120</math>, it will be easy to isolate <math>z</math> and <math>w</math>.
  4 KB (641 words) - 10:19, 6 January 2025

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