User contributions
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- 03:07, 14 December 2023 (diff | hist) . . (+513) . . N 2001 OIM Problems/Problem 1 (Created page with "== Problem == We say that a natural number <math>n</math> is "''çharrúa''" if it simultaneously satisfies the following conditions: * All digits of <math>n</math> are grea...")
- 03:02, 14 December 2023 (diff | hist) . . (-2) . . 2021 OIM Problems/Problem 6 (current)
- 03:02, 14 December 2023 (diff | hist) . . (+398) . . N 2021 OIM Problems/Problem 6 (Created page with "== Problem == Consider a regular polygon with <math>n</math> sides, <math>n \ge 4</math>, and let <math>V</math> be a subset of <math>r</math> vertices of the polygon. Show t...")
- 03:01, 14 December 2023 (diff | hist) . . (+448) . . N 2021 OIM Problems/Problem 5 (Created page with "== Problem == For a finite set <math>C</math> of integers, we define <math>S(C)</math> to be the sum of the elements of <math>C</math>. Find two nonempty sets <math>A</math>...") (current)
- 03:00, 14 December 2023 (diff | hist) . . (+303) . . N 2021 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>a,b,c,x,y,z</math> be real numbers such that <cmath>a^2+x^2=b^2+y^2=c^2+z^2=(a+b)^2+(x+y)^2=(b+c)^2+(y+z)^2=(c+a)^2+(z+x)^2</cmath> Show that <math>...") (current)
- 02:57, 14 December 2023 (diff | hist) . . (+2) . . 2021 OIM Problems/Problem 3 (current)
- 02:57, 14 December 2023 (diff | hist) . . (+572) . . N 2021 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>a_1, a_2, a_3, \cdots</math> be a sequence of positive integers and let <math>b_1, b_2, b_3, \cdots</math> be the sequence of real numbers given by <...")
- 02:53, 14 December 2023 (diff | hist) . . (+11) . . 2021 OIM Problems/Problem 2 (current)
- 02:53, 14 December 2023 (diff | hist) . . (+1,011) . . N 2021 OIM Problems/Problem 2 (Created page with "== Problem == Consider an acute triangle <math>ABC</math>, with <math>AC > AB</math>, and let <math>\Gamma</math> be its circumcircle. Let <math>E</math> and <math>F</math>...")
- 02:50, 14 December 2023 (diff | hist) . . (+2) . . 2021 OIM Problems/Problem 1 (current)
- 02:50, 14 December 2023 (diff | hist) . . (+1,032) . . N 2021 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>P = {p_1, p_2, \cdots p_{10}}</math> be a set of 10 different prime numbers and let <math>A</math> be the set of all integers greater than 1 such tha...")
- 02:45, 14 December 2023 (diff | hist) . . (+361) . . N 2022 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>\mathbb{Z}^+</math> be the set of positive integers. Find all functions <math>f: \mathbb{Z}^+ \to \mathbb{Z}^+</math> for which <cmath>f(a)f(a + b)...") (current)
- 02:42, 14 December 2023 (diff | hist) . . (+714) . . N 2022 OIM Problems/Problem 5 (Created page with "== Problem == Let <math>ABC</math> be an acute triangle with circumcircle <math>\Gamma</math>. Let <math>P</math> and <math>Q</math> be points on the half-plane defined by <m...") (current)
- 02:41, 14 December 2023 (diff | hist) . . (+1,094) . . N 2022 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>n > 2</math> be a positive integer. There is a horizontal row of <math>n</math> cells such that each cell is colored red or blue. A block is a contigu...") (current)
- 02:38, 14 December 2023 (diff | hist) . . (-2) . . 2022 OIM Problems/Problem 3 (current)
- 02:38, 14 December 2023 (diff | hist) . . (+12) . . 2022 OIM Problems/Problem 3
- 02:37, 14 December 2023 (diff | hist) . . (+463) . . N 2022 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>\mathbb{R}</math> be the set of real numbers. Find all functions <math>f : \mathbb{R} \to \mathbb{R} satisfying the following conditions simultaneousl...")
- 02:35, 14 December 2023 (diff | hist) . . (+787) . . N 2022 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>S = {13, 133, 1333, \cdots }</math> be the set of positive integers of the form <math>1\overset{n\text{-digits}}{\overbrace{3\cdots 3}}</math>, with <...") (current)
- 02:29, 14 December 2023 (diff | hist) . . (+11) . . 2022 OIM Problems/Problem 1 (current)
- 02:29, 14 December 2023 (diff | hist) . . (+635) . . N 2022 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>ABC</math> be an equilateral triangle with circumcenter <math>O</math> and circumcircle <math>\Gamma</math>. Let <math>D</math> be a point on the mino...")
- 02:24, 14 December 2023 (diff | hist) . . (+667) . . N 2023 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>P</math> be a polynomial of degree greater than or equal to 4 with integer coefficients. An integer <math>x</math> is called <math>P</math>-''represent...") (current)
- 02:21, 14 December 2023 (diff | hist) . . (+19) . . 2023 OIM Problems/Problem 5 (current)
- 02:21, 14 December 2023 (diff | hist) . . (-23) . . 2023 OIM Problems/Problem 5
- 02:20, 14 December 2023 (diff | hist) . . (+652) . . N 2023 OIM Problems/Problem 5 (Created page with "== Problem == A sequence <math>P_1, \cdots , P_n</math> of points in the plane (not necessarily distinct) is "''carioca''" if there exists a permutation <math>a_1, \cdots , a_...")
- 02:17, 14 December 2023 (diff | hist) . . (+520) . . N 2023 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>B</math> and <math>C</math> be two fixed points in the plane. For each point <math>A</math>, outside of the line <math>BC</math>, let <math>G</math> be...") (current)
- 02:15, 14 December 2023 (diff | hist) . . (+759) . . N 2023 OIM Problems/Problem 3 (Created page with "== Problem == Ana and Beto play with a two pan balance scale. They have 2023 dumbbells labeled with their weights, which are the numbers 1, 2, . . . , 2023, with none of them...") (current)
- 02:13, 14 December 2023 (diff | hist) . . (+345) . . N 2023 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>\mathbb{Z}</math> be the set of integers. Find all functions <math>f: \mathbb{Z} \to \mathbb{Z}</math> such that: <cmath>2023f(f(x))+2022x^2=2022f(x)+...") (current)
- 02:11, 14 December 2023 (diff | hist) . . (+351) . . N 2023 OIM Problems/Problem 1 (Created page with "== Problem == Let <math>n</math> be a positive integer. The following 35 multiplications are performed: <cmath>1 \cdot n,2 \cdot n,\cdots ,35 \cdot n</cmath> Show that in at...") (current)
- 00:45, 14 December 2023 (diff | hist) . . (+982) . . 1991 OIM Problems/Problem 1
- 00:39, 14 December 2023 (diff | hist) . . (0) . . 1991 OIM Problems/Problem 1
- 00:39, 14 December 2023 (diff | hist) . . (+6) . . 1991 OIM Problems/Problem 1
- 00:38, 14 December 2023 (diff | hist) . . (+31) . . 1991 OIM Problems/Problem 1
- 00:38, 14 December 2023 (diff | hist) . . (0) . . N File:1991 OIM p1.png (current)
- 00:38, 14 December 2023 (diff | hist) . . (+231) . . 1991 OIM Problems/Problem 1
- 23:54, 13 December 2023 (diff | hist) . . (+666) . . 1992 OIM Problems/Problem 1
- 23:49, 13 December 2023 (diff | hist) . . (+35) . . 1991 OIM Problems/Problem 4
- 23:48, 13 December 2023 (diff | hist) . . (+270) . . 1992 OIM Problems/Problem 1
- 23:43, 13 December 2023 (diff | hist) . . (+127) . . 1992 OIM Problems/Problem 1
- 23:41, 13 December 2023 (diff | hist) . . (+12) . . 1992 OIM Problems/Problem 1
- 23:41, 13 December 2023 (diff | hist) . . (+52) . . 1992 OIM Problems/Problem 1
- 23:40, 13 December 2023 (diff | hist) . . (+40) . . 1992 OIM Problems/Problem 1
- 23:39, 13 December 2023 (diff | hist) . . (+11) . . 1992 OIM Problems/Problem 1
- 23:39, 13 December 2023 (diff | hist) . . (+1,286) . . 1992 OIM Problems/Problem 1
- 23:29, 13 December 2023 (diff | hist) . . (+291) . . 1992 OIM Problems/Problem 1
- 23:26, 13 December 2023 (diff | hist) . . (+201) . . 1992 OIM Problems/Problem 1
- 23:23, 13 December 2023 (diff | hist) . . (+173) . . 1992 OIM Problems/Problem 1
- 22:48, 13 December 2023 (diff | hist) . . (+5) . . 1992 OIM Problems/Problem 4
- 22:47, 13 December 2023 (diff | hist) . . (-108) . . 1992 OIM Problems/Problem 4
- 22:40, 13 December 2023 (diff | hist) . . (+248) . . 1991 OIM Problems/Problem 4
- 22:38, 13 December 2023 (diff | hist) . . (+163) . . 1991 OIM Problems/Problem 4
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