User contributions
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- 15:04, 13 December 2023 (diff | hist) . . (+1) . . 1999 OIM Problems/Problem 3
- 15:04, 13 December 2023 (diff | hist) . . (+779) . . N 1999 OIM Problems/Problem 3 (Created page with "== Problem == Let there be <math>n</math> different points, <math>P_1, P_2, \cdots , P_n</math>, on a straight line of the plane (<math>n /ge 2</math>). We consider the circle...")
- 15:01, 13 December 2023 (diff | hist) . . (+623) . . N 1999 OIM Problems/Problem 2 (Created page with "== Problem == Given two circles <math>M</math> and <math>N</math>, we say that <math>M</math> bisects <math>N</math> if the common chord is a diameter of <math>N</math>. Cons...") (current)
- 14:59, 13 December 2023 (diff | hist) . . (+329) . . N 1999 OIM Problems/Problem 1 (Created page with "== Problem == Find all positive integers that are less than 1000 and satisfy the following condition: the cube of the sum of their digits is equal to the square of that intege...")
- 14:57, 13 December 2023 (diff | hist) . . (+1) . . 1998 OIM Problems/Problem 6 (current)
- 14:57, 13 December 2023 (diff | hist) . . (+11) . . 1998 OIM Problems/Problem 6
- 14:56, 13 December 2023 (diff | hist) . . (-16) . . 1998 OIM Problems/Problem 6
- 14:55, 13 December 2023 (diff | hist) . . (+18) . . 1998 OIM Problems/Problem 6
- 14:53, 13 December 2023 (diff | hist) . . (+706) . . N 1998 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>\lambda</math> be the positive root of the equation <math>t^2 - 1998t - 1 = 0</math>. The sequence <math>x_0, x_1, x_2, \cdots , x_n, \cdots</math> is...")
- 14:43, 13 December 2023 (diff | hist) . . (+477) . . N 1998 OIM Problems/Problem 5 (Created page with "== Problem == Find the maximum possible value of <math>n</math> so that there are distinct points <math>P_1, P_2, P_3, \cdots , P_n</math> in the plane and real numbers <math>...") (current)
- 14:42, 13 December 2023 (diff | hist) . . (+518) . . N 1998 OIM Problems/Problem 4 (Created page with "== Problem == Representatives of <math>n</math> countries (<math>n\ge 2</math>) are seated around a round table, so that they satisfy the following condition: if two people ar...") (current)
- 14:41, 13 December 2023 (diff | hist) . . (+481) . . N 1998 OIM Problems/Problem 3 (Created page with "== Problem == Find the minimum natural number <math>n</math> with the following property: among any <math>n</math> different numbers belonging to the set <math>{1, 2, \cdots ,...") (current)
- 14:39, 13 December 2023 (diff | hist) . . (+564) . . N 1998 OIM Problems/Problem 2 (Created page with "== Problem == The circle inscribed in the triangle <math>ABC</math> is tangent to the sides <math>BC</math>, <math>CA</math>, and <math>AB</math> at the points <math>D</math>,...") (current)
- 14:39, 13 December 2023 (diff | hist) . . (+548) . . N 1998 OIM Problems/Problem 1 (Created page with "== Problem == There are 98 points on a circle. María and José play alternately in the following way: each of them draws a segment joining two of the given points that have n...") (current)
- 14:37, 13 December 2023 (diff | hist) . . (0) . . 1997 OIM Problems/Problem 6
- 14:36, 13 December 2023 (diff | hist) . . (+612) . . N 1997 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>\textbf{P} = {P1, P2, \cdots , P_{1997}}</math> be a set of 1997 points inside a circle of radius 1, with <math>P_1</math> being the center of the cir...")
- 14:34, 13 December 2023 (diff | hist) . . (+1,035) . . N 1997 OIM Problems/Problem 5 (Created page with "== Problem == In an acute triangle <math>ABC</math>, let <math>AE</math> and <math>BF</math> be two heights, and let <math>H</math> be the orthocenter. The symmetrical line of...") (current)
- 14:31, 13 December 2023 (diff | hist) . . (+814) . . N 1997 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>n</math> be a positive integer. Let us consider the sum <math>x_1y_1 + x_2y_2 + \cdots + x_ny_n</math>, where the values that the variables <math>x_1,...")
- 14:26, 13 December 2023 (diff | hist) . . (+1) . . 1997 OIM Problems/Problem 3 (current)
- 14:26, 13 December 2023 (diff | hist) . . (+3) . . 1997 OIM Problems/Problem 3
- 14:26, 13 December 2023 (diff | hist) . . (+875) . . N 1997 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>n \le 2</math> be an integer and <math>D_n</math> be the set of points <math>(x, y)</math> of the plane whose coordinates are integers with <cmath>-n...")
- 14:23, 13 December 2023 (diff | hist) . . (+1,144) . . N 1997 OIM Problems/Problem 2 (Created page with "== Problem == With the center at the incenter <math>I</math> of a triangle <math>ABC</math>, a circle is drawn that cuts each of the three sides of the triangle at two points:...") (current)
- 14:19, 13 December 2023 (diff | hist) . . (+679) . . N 1997 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>r \ge 1</math> be a real number that satisfies the following property: For each pair of positive integers <math>m</math> and <math>n</math>, with <mat...") (current)
- 14:16, 13 December 2023 (diff | hist) . . (+660) . . N 1996 OIM Problems/Problem 6 (Created page with "== Problem == There are <math>n</math> different points <math>A_1, \cdots , A_n</math> in the plane and each point <math>A_i</math> has been assigned a real number <math>\lamb...") (current)
- 14:12, 13 December 2023 (diff | hist) . . (+19) . . 1996 OIM Problems/Problem 5 (current)
- 14:11, 13 December 2023 (diff | hist) . . (+3) . . 1996 OIM Problems/Problem 5
- 14:11, 13 December 2023 (diff | hist) . . (0) . . N File:Ibe11 2.gif (current)
- 14:11, 13 December 2023 (diff | hist) . . (+1,095) . . N 1996 OIM Problems/Problem 5 (Created page with "== Problem == Three pieces <math>A</math>, <math>B</math> and <math>C</math> are located one at each vertex of an equilateral triangle of side <math>n</math>. The triangle has...")
- 14:05, 13 December 2023 (diff | hist) . . (+492) . . N 1996 OIM Problems/Problem 4 (Created page with "== Problem == Given a natural number <math>n \ge 2</math>, consider all fractions of the form <math>\frac{1}{ab}</math>, where <math>a</math> and <math>b</math> are natural nu...") (current)
- 14:04, 13 December 2023 (diff | hist) . . (+606) . . N 1996 OIM Problems/Problem 3 (Created page with "== Problem == We have a board of <math>k^2-k+1</math> rows and <math>k^2-k+1</math> columns, where <math>k=p+1</math> and <math>p</math> is a prime number. For each prime <mat...") (current)
- 14:02, 13 December 2023 (diff | hist) . . (+634) . . N 1996 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>M</math> be the midpoint of the median <math>AD</math> of triangle <math>ABC</math> (<math>D</math> belongs to side <math>BC</math>). The line <math>BM...") (current)
- 13:59, 13 December 2023 (diff | hist) . . (+363) . . N 1996 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>n</math> be a natural number. A cube with edge <math>n</math> can be divided into 1996 cubes whose edges are also natural numbers. Determine the smalle...")
- 13:57, 13 December 2023 (diff | hist) . . (+13) . . 1995 OIM Problems/Problem 6 (current)
- 13:57, 13 December 2023 (diff | hist) . . (+4) . . 1995 OIM Problems/Problem 6
- 13:56, 13 December 2023 (diff | hist) . . (0) . . 1995 OIM Problems/Problem 6
- 13:56, 13 December 2023 (diff | hist) . . (+834) . . N 1995 OIM Problems/Problem 6 (Created page with "== Problem == A function <math>f: N \to N</math> is circular if for every <math>p</math> in <math>N</math> there exists <math>n</math> in <math>N</math> with <math>n \le p</ma...")
- 13:51, 13 December 2023 (diff | hist) . . (+635) . . N 1995 OIM Problems/Problem 5 (Created page with "== Problem == The circle inscribed in the triangle <math>ABC</math> is tangent to <math>BC</math>, <math>CA</math>, and <math>AB</math> at <math>D</math>, <math>E</math>, and...") (current)
- 13:50, 13 December 2023 (diff | hist) . . (+558) . . N 1995 OIM Problems/Problem 4 (Created page with "== Problem == Pieces are placed on a board with <math>m \times n</math> squares. Each piece placed on the board "''dominates''" all the squares in the row (-), column (|) and...") (current)
- 13:48, 13 December 2023 (diff | hist) . . (-4) . . 1995 OIM Problems/Problem 3 (current)
- 13:48, 13 December 2023 (diff | hist) . . (+771) . . N 1995 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>r</math> and <math>s</math> be two orthogonal lines that are not in the same plane. Let <math>AB</math> be their common perpendicular, such that <math>...")
- 13:45, 13 December 2023 (diff | hist) . . (+1) . . 1995 OIM Problems/Problem 2 (current)
- 13:44, 13 December 2023 (diff | hist) . . (0) . . 1995 OIM Problems/Problem 2
- 13:44, 13 December 2023 (diff | hist) . . (-261) . . 1995 OIM Problems/Problem 2
- 13:44, 13 December 2023 (diff | hist) . . (+746) . . N 1995 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>n</math> be an integer greater than 1. Determine the real numbers <cmath>X_1, X_2, \cdots ,X_n \ge 1,\;\text{and}\; X+{n+1} > 0</cmath> that verify t...")
- 13:39, 13 December 2023 (diff | hist) . . (+245) . . N 1995 OIM Problems/Problem 1 (Created page with "== Problem == Determine the possible values of the sums of the digits of all perfect squares. ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com == Solution == {{...") (current)
- 13:37, 13 December 2023 (diff | hist) . . (+646) . . N 1994 OIM Problems/Problem 6 (Created page with "== Problem == Show that every natural number <math>n \le 2^{1,000,000}</math> can be obtained after 1 by doing less than 1,100,000 additions; more precisely, there is a finite...") (current)
- 13:32, 13 December 2023 (diff | hist) . . (0) . . 1994 OIM Problems/Problem 5 (current)
- 13:31, 13 December 2023 (diff | hist) . . (+789) . . N 1994 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>n</math> and <math>r</math> be two positive integers. We wish to construct <math>r</math> subsets <math>A_1, A_2, \cdots , A_r</math> of <math>{0,1,......")
- 13:29, 13 December 2023 (diff | hist) . . (+604) . . N 1994 OIM Problems/Problem 4 (Created page with "== Problem == Points <math>A</math>, <math>B</math> and <math>C</math> are given on a circle <math>K</math> so that triangle <math>ABC</math> is acute. Let <math>P</math> be a...") (current)
- 13:28, 13 December 2023 (diff | hist) . . (+654) . . N 1994 OIM Problems/Problem 3 (Created page with "== Problem == In each square of an <math>n \times n</math> board there is a lamp. When a lamp is touched, it and all the lamps located in the row and column where that lamp be...") (current)
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