# New pages

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- 16:02, 7 December 2023 Bisector (hist) [2,098 bytes] Vvsss (talk | contribs) (Created page with "==Division of bisector== Let a triangle <math>\triangle ABC, BC = a, AC = b, AB = c</math> be given. Let <math>AA', BB',</math> and <math>CC'</math> be the bisectors of <math>...")
- 13:06, 5 December 2023 Redelephant876 (hist) [753 bytes] Redelephant876 (talk | contribs) (Created page with "redelephant876 is an AoPS user Joined: Dec. 4th, 2018 Blog: https://artofproblemsolving.com/community/c3624588 *Still a work in progress* Forum: https://artofproblemsolving...")
- 07:51, 5 December 2023 2014 Indonesia MO Problems/Problem 1 (hist) [2 bytes] The eureka (talk | contribs) (Created page with "hi")
- 13:29, 2 December 2023 Extraneous solutions (hist) [0 bytes] Ddk001 (talk | contribs) (Created page with "Extraneous solutions are solutions that does not satisfy the original equation.")
- 08:18, 1 December 2023 Useretaxi42ru (hist) [890 bytes] Etaxi42ru (talk | contribs) (Created page with "Вы ищете надежный и выгодный способ заработка? Тогда аренда авто для такси - это то, что вам нужн...")
- 19:36, 30 November 2023 Decreasing (hist) [638 bytes] Kimilao (talk | contribs) (Added the decreasing page.)
- 08:51, 30 November 2023 Nonincreasing (hist) [649 bytes] Kimilao (talk | contribs) (Added the nonincreasing page.)
- 23:50, 29 November 2023 Michigan Math Meet (hist) [1,078 bytes] Andyf (talk | contribs) (Created page with "'''Michigan Math Meet ''' is an annual high school mathematics competition organized by University of Michigan undergraduates. This competition is held every March at the Univ...")
- 16:29, 28 November 2023 Schoolhouse (hist) [106 bytes] Smartduck68 (talk | contribs) (Created page with "This is the page for the AoPS Schoolhouse. If you are here on accident, please see “AoPS Schoolhouse”.")
- 23:08, 27 November 2023 2024 AMC 8 Problems/Problem 23 (hist) [4 bytes] Chencanada23 (talk | contribs) (Created page with "Test")
- 19:53, 27 November 2023 An Introduction to Gmaasology (hist) [50 bytes] Gamer doge543 (talk | contribs) (Created page with "Only gmaas knows this..")
- 00:19, 27 November 2023 2013 Canadian MO Problems/Problem 5 (hist) [468 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Let <math>O</math> denote the circumcentre of an acute-angled triangle <math>ABC</math>. Let point <math>P</math> on side <math>AB</math> be such that <math>\angl...")
- 00:18, 27 November 2023 2013 Canadian MO Problems/Problem 4 (hist) [5,673 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Let <math>n</math> be a positive integer. For any positive integer <math>j</math> and positive real number <math>r</math>, define <cmath> f_j(r) =\min (jr, n)+\m...")
- 00:18, 27 November 2023 2013 Canadian MO Problems/Problem 3 (hist) [493 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Let <math>G</math> be the centroid of a right-angled triangle <math>ABC</math> with <math>\angle BCA = 90^\circ</math>. Let <math>P</math> be the point on ray <ma...")
- 00:18, 27 November 2023 2013 Canadian MO Problems/Problem 2 (hist) [390 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == The sequence <math>a_1, a_2, \dots, a_n</math> consists of the numbers <math>1, 2, \dots, n</math> in some order. For which positive integers <math>n</math> is it...")
- 23:32, 26 November 2023 2013 Canadian MO Problems/Problem 1 (hist) [4,240 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Determine all polynomials <math>P(x)</math> with real coefficients such that <cmath>(x+1)P(x-1)-(x-1)P(x)</cmath> is a constant polynomial. ==Solution== Le...")
- 21:29, 26 November 2023 2014 Canadian MO Problems/Problem 5 (hist) [589 bytes] Tomasdiaz (talk | contribs) (Created page with "== Problem == Fix positive integers <math>n</math> and <math>k\ge 2</math>. A list of n integers is written in a row on a blackboard. You can choose a contiguous block of inte...")
- 21:28, 26 November 2023 2014 Canadian MO Problems/Problem 4 (hist) [502 bytes] Tomasdiaz (talk | contribs) (Created page with "== Problem== The quadrilateral <math>ABCD</math> is inscribed in a circle. The point <math>P</math> lies in the interior of <math>ABCD</math>, and <math>\angle P AB = \angle P...")
- 21:28, 26 November 2023 2014 Canadian MO Problems/Problem 3 (hist) [465 bytes] Tomasdiaz (talk | contribs) (Created page with "== Problem == Let <math>p</math> be a fixed odd prime. A <math>p</math>-tuple <math>(a_1,a_2,a_3,\ldots,a_p)</math> of integers is said to be good if (i) <math>0\le a_i\le p...")
- 21:27, 26 November 2023 2014 Canadian MO Problems/Problem 2 (hist) [567 bytes] Tomasdiaz (talk | contribs) (Created page with "== Problem== Let <math>m</math> and <math>n</math> be odd positive integers. Each square of an <math>m</math> by <math>n</math> board is coloured red or blue. A row is said to...")
- 21:37, 25 November 2023 Mediant theorem (hist) [1,239 bytes] Kscv (talk | contribs) (Created page with "''Not to be confused with median.'' ==Definition== The '''mediant''' of two fractions <math>\frac{a}{c}</math> and <math>\frac{b}{d}</math> is defined as <math>\frac{a+b...")
- 10:34, 25 November 2023 Divisibility rules/Rule 2 for 13 proof (hist) [1,537 bytes] Thurinalas (talk | contribs) (Created page with "== Proof == ''This is based on divisibility by 11 rule or divisibility by 7 rule '' As...")
- 10:30, 25 November 2023 Divisibility rules/Rule 1 for 7 proof (hist) [1,308 bytes] Thurinalas (talk | contribs) (first draft)
- 09:27, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 15 (hist) [751 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== For any finite sequence of positive integers <math>A=(a_1,a_2,\cdots,a_n)</math>, let <math>f(A)</math> be the sequence of the differences between consecutive term...")
- 09:26, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 14 (hist) [524 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== A rational <math>\frac{1}{k}</math>, where <math>k</math> is a positive integer, is said to be <math>\textit{n-unsound}</math> if its base <math>N</math> represent...")
- 09:26, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 13 (hist) [1,767 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Consider two circles of different sizes that do not intersect. The smaller circle has center <math>O</math>. Label the intersection of their common external tang...")
- 09:25, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 12 (hist) [1,052 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>x_k</math> be the largest positive rational solution <math>x</math> to the equation <math>(2007-x)(x+2007^{-k})^k=1</math> for all integers <math>k\ge 2<...")
- 09:25, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 11 (hist) [1,486 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Each face of an octahedron is randomly colored blue or red. A caterpillar is on a vertex of the octahedron and wants to get to the opposite vertex by traversing t...")
- 09:24, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 10 (hist) [4,036 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Given a point <math>P</math> in the coordinate plane, let <math>T_k(P)</math> be the <math>90^\circ</math> rotation of <math>P</math> around the point <math>(2000-...")
- 09:24, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 9 (hist) [2,138 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== <math>ABC</math> is a triangle with integer side lengths. Extend <math>\overline{AC}</math> beyond <math>C</math> to point <math>D</math> such that <math>CD=120</...")
- 09:23, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 8 (hist) [1,564 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== A sequence of positive reals defined by <math>a_0=x</math>, <math>a_1=y</math>, and <math>a_n\cdot a_{n+2}=a_{n+1}</math> for all integers <math>n\ge 0</math>. Gi...")
- 09:23, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 7 (hist) [2,729 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Let <math>P_n(x)=1+x+x^2+\cdots+x^n</math> and <math>Q_n(x)=P_1\cdot P_2\cdots P_n</math> for all integers <math>n\ge 1</math>. How many more distinct complex ro...")
- 09:22, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 6 (hist) [558 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == <math>C_1</math> is a circle with radius <math>164</math> and <math>C_2</math> is a circle internally tangent to <math>C_1</math> that passes through the center o...")
- 09:22, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 5 (hist) [6,013 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>S(n)</math> be the sum of the squares of the digits of <math>n</math>. How many positive integers <math>n>2007</math> satisfy the inequality <math>n-S(n...")
- 09:21, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 4 (hist) [280 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>R</math> be a set of <math>13</math> points in the plane, no three of which lie on the same line. At most how many ordered triples of points <math>(A,B,...")
- 09:18, 23 November 2023 Mock AIME 6 2006-2007 Problems/Problem 2 (hist) [1,003 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem == Draw in the diagonals of a regular octagon. What is the sum of all distinct angle measures, in degrees, formed by the intersections of the diagonals in the int...")
- 16:20, 22 November 2023 2024 AMC 8 Problems/Problem 9 (hist) [12 bytes] Adam22 (talk | contribs) (Created page with "don't cheat!")
- 16:18, 22 November 2023 2024 AIME I Problems/Problem 2 (hist) [36 bytes] Adam22 (talk | contribs) (Created page with "xoink xonks xonk xoinks xionk xoinks")
- 16:15, 22 November 2023 2025 AIME II (hist) [4 bytes] Adam22 (talk | contribs) (Created page with "duck")
- 12:54, 22 November 2023 2023 USAJMO Problems/Problem 6 (hist) [727 bytes] Eevee9406 (talk | contribs) (Created page with "==Problem== Isosceles triangle <math>ABC</math>, with <math>AB=AC</math>, is inscribed in circle <math>\omega</math>. Let <math>D</math> be an arbitrary point inside <math>BC<...")
- 12:54, 22 November 2023 2023 USAJMO Problems/Problem 5 (hist) [841 bytes] Eevee9406 (talk | contribs) (Created page with "==Problem== A positive integer <math>a</math> is selected, and some positive integers are written on a board. Alice and Bob play the following game. On Alice's turn, she must...")
- 00:26, 22 November 2023 1994 IMO Problems/Problem 6 (hist) [439 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Show that there exists a set <math>A</math> of positive integers with the following property: For any infinite set <math>S</math> of primes there exist two positi...")
- 09:28, 21 November 2023 2024 AMC 8 Problems/Problem 8 (hist) [16 bytes] Gavin deng (talk | contribs) (Created page with "To be determined")
- 15:44, 20 November 2023 1996 IMO Problems/Problem 6 (hist) [574 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>p, q, n</math> be three positive integers with <math>p+q<n</math>. Let <math>(x_0,x_1,\cdots ,x_n)</math> be an <math>(n+1)</math>-tuple of integers sat...")
- 08:04, 20 November 2023 Korean Mathematical Olympiad (hist) [1,265 bytes] Kscv (talk | contribs) (Created page with "The Korean Mathematical Olympiad (KMO) is the national mathematical olympiad of South Korea. == Format of the Competition == The KMO consists of two stages (Stage I and Sta...")
- 23:48, 18 November 2023 2003 IMO Problems/Problem 5 (hist) [1,108 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>n</math> be a positive integer and let <math>x_1 \le x_2 \le \cdots \le x_n</math> be real numbers. Prove that <cmath>\left( \sum_{i=1}^{n}\sum_{j=i}^{...")
- 23:44, 18 November 2023 2003 IMO Problems/Problem 4 (hist) [507 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>ABCD</math> be a cyclic quadrilateral. Let <math>P</math>, <math>Q</math>, and <math>R</math> be the feet of perpendiculars from <math>D</math> to lines...")
- 23:40, 18 November 2023 2003 IMO Problems/Problem 3 (hist) [304 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Each pair of opposite sides of convex hexagon has the property that the distance between their midpoints is <math>\frac{\sqrt{3}}{2}</math> times the sum of their...")
- 23:38, 18 November 2023 2002 IMO Problems/Problem 6 (hist) [409 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Let <math>n \ge 3</math> be a positive integer. Let <math>C_1,C_2,...,C_n</math> be unit circles in the plane, with centers <math>O_1,O_2,...,O_n</math> respecti...")
- 23:34, 18 November 2023 2002 IMO Problems/Problem 5 (hist) [256 bytes] Tomasdiaz (talk | contribs) (Created page with "==Problem== Find all functions <math>f:\Bbb{R}\to \Bbb{R}</math> such that <cmath>(f(x)+f(z))(f(y)+f(t))=f(xy-zt)+f(xt+yz)</cmath> for all real numbers <math>x,y,z,t</math>...")