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• 13:02, 14 December 2023 (diff | hist) . . (+378)‎ . . N 2019 OIM Problems/Problem 2 ‎ (Created page with "== Problem == Find all polynomials <math>P(x)</math> of degree <math>n \ge 1</math> with integer coefficients such that for every real number <math>x</math> it holds <cmath>P...") (current)
• 13:00, 14 December 2023 (diff | hist) . . (+397)‎ . . N 2019 OIM Problems/Problem 1 ‎ (Created page with "== Problem == For each positive integer <math>n</math>, let <math>s(n)</math> be the sum of the squares of the digits of <math>n</math>. For example, <math>s(15) = 1^2 + 5^2 =...") (current)
• 12:59, 14 December 2023 (diff | hist) . . (+819)‎ . . N 2020 OIM Problems/Problem 6 ‎ (Created page with "== Problem == Let <math>ABC</math> be an acute and scalene triangle. Let <math>H</math> be the orthocenter and <math>O</math> the circumcenter of triangle <math>ABC</math>, an...") (current)
• 12:57, 14 December 2023 (diff | hist) . . (+309)‎ . . N 2020 OIM Problems/Problem 5 ‎ (Created page with "== Problem == Find all functions <math>f : \mathbb{R} \to \mathbb{R}</math> such that <cmath>f(xf(x-y))+yf(x)=x+y+f(x^2)</cmath> for any real numbers <math>x, y</math>. ~tr...") (current)
• 12:55, 14 December 2023 (diff | hist) . . (+572)‎ . . N 2020 OIM Problems/Problem 4 ‎ (Created page with "== Problem == Prove that there exists a set <math>C</math> of 2020 positive and distinct integers that simultaneously fulfills the following properties: * When we calculate...") (current)
• 12:53, 14 December 2023 (diff | hist) . . (+15)‎ . . 2020 OIM Problems/Problem 3 ‎
• 12:52, 14 December 2023 (diff | hist) . . (+1)‎ . . 2020 OIM Problems/Problem 3 ‎
• 12:52, 14 December 2023 (diff | hist) . . (+987)‎ . . N 2020 OIM Problems/Problem 3 ‎ (Created page with "== Problem == Let <math>n \ge 2</math> be an integer. A sequence <math>\alpha = (a_1, a_2, \cdots , a_n)</math> of <math>n</math> integers is "''Limeña''" (from Lima, Perú)...")
• 12:45, 14 December 2023 (diff | hist) . . (+608)‎ . . N 2020 OIM Problems/Problem 2 ‎ (Created page with "== Problem == For each positive integer <math>n</math>, define <math>T_n</math> as the smallest positive integer such that <math>1 + 2 + \cdots + T_n</math> is a multiple of <...") (current)
• 12:43, 14 December 2023 (diff | hist) . . (+305)‎ . . 2020 OIM Problems/Problem 1 ‎ (current)
• 12:40, 14 December 2023 (diff | hist) . . (+542)‎ . . N 2020 OIM Problems/Problem 1 ‎ (Created page with "== Problem == Let ABC be an acute triangle such that AB < AC. The midpoints of the Sides AB and AC are M and N, respectively. Let P and Q be points on the line MN such that \C...")
• 12:35, 14 December 2023 (diff | hist) . . (+851)‎ . . N 2015 OIM Problems/Problem 6 ‎ (Created page with "== Problem == Beto plays the following game with his computer: initially his computer randomly chooses 30 numbers from 1 to 2015, and Beto writes them on a blackboard (there m...")
• 12:33, 14 December 2023 (diff | hist) . . (+217)‎ . . N 2015 OIM Problems/Problem 5 ‎ (Created page with "== Problem == Find all pairs <math>(a, b)</math> of integers that verify: <cmath>(b^2+7(a-b))^2=a^3b</cmath> ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com =...")
• 12:32, 14 December 2023 (diff | hist) . . (+663)‎ . . N 2015 OIM Problems/Problem 4 ‎ (Created page with "== Problem == In acute triangle <math>ABC</math>, point <math>D</math> is the foot of the perpendicular from <math>A</math> on side <math>BC</math>. Let <math>P</math> be a po...")
• 12:30, 14 December 2023 (diff | hist) . . (+554)‎ . . N 2015 OIM Problems/Problem 3 ‎ (Created page with "== Problem == Let <math>\alpha</math> and <math>\beta</math> be roots of the polynomial <math>x^2-qx+1</math>, where <math>q</math> is a rational number greater than 2. We de...")
• 12:24, 14 December 2023 (diff | hist) . . (+523)‎ . . N 2015 OIM Problems/Problem 2 ‎ (Created page with "== Problem == A line <math>r</math> contains the points <math>A</math>, <math>B</math>, <math>C</math> and <math>D</math> in that order. Let <math>P</math> be a point outside...")
• 12:22, 14 December 2023 (diff | hist) . . (+308)‎ . . N 2015 OIM Problems/Problem 1 ‎ (Created page with "== Problem == The number 125 can be represented as the sum of several natural numbers that are greater than 1 and coprime two to two. Find the maximum number of sums that can...")
• 03:50, 14 December 2023 (diff | hist) . . (0)‎ . . 2002 OIM Problems/Problem 6 ‎ (current)
• 03:49, 14 December 2023 (diff | hist) . . (0)‎ . . 2002 OIM Problems/Problem 6 ‎
• 03:49, 14 December 2023 (diff | hist) . . (+524)‎ . . 2002 OIM Problems/Problem 6 ‎
• 03:45, 14 December 2023 (diff | hist) . . (+2)‎ . . 2002 OIM Problems/Problem 5 ‎ (current)
• 03:45, 14 December 2023 (diff | hist) . . (-242)‎ . . 2002 OIM Problems/Problem 5 ‎
• 03:43, 14 December 2023 (diff | hist) . . (-1)‎ . . 2002 OIM Problems/Problem 4 ‎ (→‎Problem) (current)
• 03:43, 14 December 2023 (diff | hist) . . (+40)‎ . . 2002 OIM Problems/Problem 4 ‎
• 03:41, 14 December 2023 (diff | hist) . . (+12)‎ . . 2002 OIM Problems/Problem 3 ‎ (current)
• 03:41, 14 December 2023 (diff | hist) . . (-644)‎ . . 2002 OIM Problems/Problem 3 ‎
• 03:39, 14 December 2023 (diff | hist) . . (-290)‎ . . 2002 OIM Problems/Problem 2 ‎ (current)
• 03:38, 14 December 2023 (diff | hist) . . (-3)‎ . . 2002 OIM Problems/Problem 1 ‎ (current)
• 03:37, 14 December 2023 (diff | hist) . . (-125)‎ . . 2002 OIM Problems/Problem 1 ‎
• 03:35, 14 December 2023 (diff | hist) . . (-5)‎ . . 2003 OIM Problems/Problem 6 ‎ (current)
• 03:34, 14 December 2023 (diff | hist) . . (-1)‎ . . 2003 OIM Problems/Problem 6 ‎
• 03:34, 14 December 2023 (diff | hist) . . (+1)‎ . . 2003 OIM Problems/Problem 6 ‎
• 03:33, 14 December 2023 (diff | hist) . . (+469)‎ . . N 2003 OIM Problems/Problem 6 ‎ (Created page with "== Problem == Sequences <math>(a_n</math>)_{n \ge 0}, and <math>(b_n)_{n \ge 0}</math> with are defined by: <cmath>a_0=1 \text{, }b_0=4\text{, and}</cmath> <cmath>a_{n+1}=a_...")
• 03:32, 14 December 2023 (diff | hist) . . (+644)‎ . . N 2003 OIM Problems/Problem 5 ‎ (Created page with "== Problem == In the square <math>ABCD</math>, let <math>P</math> and <math>Q</math> be points belonging to the sides <math>BC</math> and <math>CD</math> respectively, differe...") (current)
• 03:32, 14 December 2023 (diff | hist) . . (+547)‎ . . N 2003 OIM Problems/Problem 4 ‎ (Created page with "== Problem == Let <math>M = {1, 2, \cdots , 49}</math> be the set of the first <math>49</math> positive integers. Determine the maximum integer <math>k</math> such that the se...") (current)
• 03:31, 14 December 2023 (diff | hist) . . (+1,102)‎ . . N 2003 OIM Problems/Problem 3 ‎ (Created page with "== Problem == Pablo was copying the following problem from a blackboard: <cmath>\textit{Consider all sequences of 2004 real numbers }(x_0,x_1,x_2,\cdots , x_{2003})\textit{,...") (current)
• 03:30, 14 December 2023 (diff | hist) . . (+672)‎ . . N 2003 OIM Problems/Problem 2 ‎ (Created page with "== Problem == Let <math>C</math> and <math>D</math> be two points on the semicircle of diameter <math>AB</math> such that <math>B</math> and <math>C</math> are in different se...") (current)
• 03:29, 14 December 2023 (diff | hist) . . (+684)‎ . . N 2003 OIM Problems/Problem 1 ‎ (Created page with "== Problem == a) There are two sequences, each of 2003 consecutive integers, and a board with 2 rows and 2003 columns Decide if it is always possible to distribute the numbe...")
• 03:27, 14 December 2023 (diff | hist) . . (+249)‎ . . N 2001 OIM Problems/Problem 6 ‎ (Created page with "== Problem == Prove that it is impossible to cover a square of side 1 with five equal squares with sides less than <math>\frac{1}{2}</math> ~translated into English by Toma...") (current)
• 03:26, 14 December 2023 (diff | hist) . . (0)‎ . . 2001 OIM Problems/Problem 5 ‎ (current)
• 03:25, 14 December 2023 (diff | hist) . . (0)‎ . . 2001 OIM Problems/Problem 5 ‎
• 03:25, 14 December 2023 (diff | hist) . . (+1)‎ . . 2001 OIM Problems/Problem 5 ‎
• 03:24, 14 December 2023 (diff | hist) . . (-4)‎ . . 2001 OIM Problems/Problem 5 ‎
• 03:24, 14 December 2023 (diff | hist) . . (+12)‎ . . 2001 OIM Problems/Problem 5 ‎
• 03:23, 14 December 2023 (diff | hist) . . (+1,437)‎ . . N 2001 OIM Problems/Problem 5 ‎ (Created page with "== Problem == On a <math>2000 \times 2001</math> board the squares have coordinates <math>(x, y)</math> with <math>x, y</math> integers, <math>0 \le x le 1999</math> and <mat...")
• 03:16, 14 December 2023 (diff | hist) . . (+498)‎ . . N 2001 OIM Problems/Problem 4 ‎ (Created page with "== Problem == Find the maximum number of increasing arithmetic progressions of three terms that can have a sequence <math>a_1 < a_2 < \cdots < a_n</math> of <math>n \ge 3</ma...") (current)
• 03:12, 14 December 2023 (diff | hist) . . (+12)‎ . . 2001 OIM Problems/Problem 3 ‎ (current)
• 03:12, 14 December 2023 (diff | hist) . . (+550)‎ . . N 2001 OIM Problems/Problem 3 ‎ (Created page with "== Problem == Let <math>S</math> be a set of <math>n</math> elements and <math>S_1, S_2, \cdots , S_k</math> subsets of <math>S</math> (<math>k \ge 2</math>), such that each...")
• 03:09, 14 December 2023 (diff | hist) . . (+635)‎ . . N 2001 OIM Problems/Problem 2 ‎ (Created page with "== Problem == The circle inscribed in the triangle <math>ABC</math> has center <math>O</math> and is tangent to the sides <math>BC</math>, <math>AC</math> and <math>AB</math>...") (current)
• 03:08, 14 December 2023 (diff | hist) . . (0)‎ . . 2001 OIM Problems/Problem 1 ‎ (current)

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