User contributions
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- 12:27, 13 December 2023 (diff | hist) . . (+122) . . 1987 OIM Problems/Problem 3 (current)
- 12:26, 13 December 2023 (diff | hist) . . (+63) . . 1987 OIM Problems/Problem 2 (current)
- 12:26, 13 December 2023 (diff | hist) . . (+59) . . 1987 OIM Problems/Problem 2
- 12:26, 13 December 2023 (diff | hist) . . (+122) . . 1987 OIM Problems/Problem 1
- 12:25, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 6 (current)
- 12:25, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 5
- 12:25, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 4
- 12:25, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 3
- 12:25, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 2
- 12:24, 13 December 2023 (diff | hist) . . (+122) . . 1985 OIM Problems/Problem 1
- 12:24, 13 December 2023 (diff | hist) . . (+277) . . N 1989 OIM Problems/Problem 6 (Created page with "== Problem == Prove that there's and infinity of pairs of natural numbers that satisfy the equation: <math>2x^2-3x=3y^2</math> ~translated into English by Tomas Diaz. ~orders...") (current)
- 12:23, 13 December 2023 (diff | hist) . . (+59) . . 1989 OIM Problems/Problem 5 (current)
- 12:22, 13 December 2023 (diff | hist) . . (+301) . . N 1989 OIM Problems/Problem 5 (Created page with "== Problem == Let function <math>f</math> defined over set {1; 2; 3; ... } (i) <math>f(1)=1</math> (ii) <math>f(2n+1)=f(2n)+1</math> (iii) <math>f(2n)=3f(n)</math> Find th...")
- 12:20, 13 December 2023 (diff | hist) . . (+520) . . N 1989 OIM Problems/Problem 4 (Created page with "== Problem == The circumference inscribed in triangle <math>ABC</math>, is tangent to sides <math>AB</math> and <math>AC</math> at points <math>M</math> and <math>N</math> res...")
- 12:19, 13 December 2023 (diff | hist) . . (0) . . 1989 OIM Problems/Problem 2
- 12:18, 13 December 2023 (diff | hist) . . (+2) . . 1989 OIM Problems/Problem 2
- 12:18, 13 December 2023 (diff | hist) . . (+44) . . 1989 OIM Problems/Problem 2
- 12:16, 13 December 2023 (diff | hist) . . (+290) . . N 1989 OIM Problems/Problem 3 (Created page with "== Problem == Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle. Prove: <cmath>\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+...")
- 12:16, 13 December 2023 (diff | hist) . . (+1) . . 1989 OIM Problems/Problem 2
- 12:15, 13 December 2023 (diff | hist) . . (+289) . . N 1989 OIM Problems/Problem 2 (Created page with "== Problem == ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com Let <math>a</math>, <math>b</math>, and <math>c</math> be the longitudes of the sides of a triangle...")
- 12:13, 13 December 2023 (diff | hist) . . (+199) . . N 1989 OIM Problems/Problem 1 (Created page with "== Problem == Find all triples of real numbers that satisfy the system of equations: <cmath>x+y-z=-1</cmath> <cmath>x^2-k^2+z^2=1</cmath> <cmath>-x^3+y^3+z^3=-1</cmath> ==...")
- 12:11, 13 December 2023 (diff | hist) . . (+268) . . N 1988 OIM Problems/Problem 6 (Created page with "== Problem == Consider the sets of <math>n</math> natural numbers different than zero out of which there are not three elements in arithmetic progression. Prove that in one o...")
- 12:09, 13 December 2023 (diff | hist) . . (+389) . . N 1988 OIM Problems/Problem 5 (Created page with "== Problem == Consider expressions in the form: <math>x+yt+zt^2</math> with <math>x</math>, <math>y</math>, and <math>z</math> rational numbers and <math>t^3=2</math>. Prove...")
- 12:07, 13 December 2023 (diff | hist) . . (+1) . . 1988 OIM Problems/Problem 4
- 12:06, 13 December 2023 (diff | hist) . . (+12) . . 1988 OIM Problems/Problem 4
- 12:06, 13 December 2023 (diff | hist) . . (+417) . . N 1988 OIM Problems/Problem 4 (Created page with "== Problem == Let <math>ABC</math> be a triangle which sides are <math>a</math>, <math>b</math>, <math>c</math>. We divide each side of the triangle in <math>n</math> equal s...")
- 12:03, 13 December 2023 (diff | hist) . . (+220) . . N 1988 OIM Problems/Problem 3 (Created page with "== Problem == Prove that from all triangles whose vertices are 3, 5 and 7, away from a given point <math>P</math>, that the one with the largest perimeter has <math>P</math>...")
- 12:01, 13 December 2023 (diff | hist) . . (+12) . . 1988 OIM Problems/Problem 2 (→Problem)
- 12:01, 13 December 2023 (diff | hist) . . (+341) . . N 1988 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>a</math>, <math>b</math>, <math>c</math>, <math>d</math>, <math>p</math>, and <math>q</math>, be non-zero natural numbers that verify <math>ad-bc=1</ma...")
- 11:58, 13 December 2023 (diff | hist) . . (+245) . . N 1988 OIM Problems/Problem 1 (Created page with "== Problem == The measurements of the sides of a triangle are in arithmetic progression and the lengths of the heights of the same triangle are also in arithmetic progression....")
- 11:57, 13 December 2023 (diff | hist) . . (+388) . . N 1987 OIM Problems/Problem 6 (Created page with "== Problem == Let <math>ABCD</math> be a planar convex quadrilateral, <math>P</math> and <math>QQ</math> are points of <math>AD</math> and <math>BC</math> respectively such th...")
- 11:54, 13 December 2023 (diff | hist) . . (+462) . . N 1987 OIM Problems/Problem 5 (Created page with "== Problem == If <math>r</math>, <math>s</math>, and <math>t</math> are all the roots of the equation: <cmath>x(x-2)3x-7)=2</cmath> (a) Prove that <math>r</math>, <math>s</ma...")
- 11:51, 13 December 2023 (diff | hist) . . (+327) . . N 1987 OIM Problems/Problem 4 (Created page with "== Problem == We define the succession <math>p_n</math> the following way: <math>p_1=2</math> and for all <math>n</math> more or equal than 2, <math>p_n</math> is the greatest...")
- 11:49, 13 December 2023 (diff | hist) . . (-1) . . 1987 OIM Problems/Problem 3 (→Problem)
- 11:49, 13 December 2023 (diff | hist) . . (+234) . . N 1987 OIM Problems/Problem 3 (Created page with "== Problem == Prove that if <math>m</math>, <math>n</math>, and <math>r</math> are non-zero positive integers, and <cmath>1+m+n\sqrt{3}=\[2+\sqrt{3}]^{2r-1}</cmath> then <math...")
- 11:47, 13 December 2023 (diff | hist) . . (+419) . . N 1987 OIM Problems/Problem 2 (Created page with "== Problem == On a triangle <math>ABC</math>, <math>M</math> and <math>N</math> are the respective midpoints of sides <math>AC</math> and <math>AB</math>, and <math>P</math> i...")
- 11:45, 13 December 2023 (diff | hist) . . (+224) . . N 1987 OIM Problems/Problem 1 (Created page with "== Problem == Find all <math>f(x)</math> such that: <cmath>\left[ f(x) \right]^2f\left( \frac{1-x}{1+x} \right)=64x</cmath> for <math>x \ne 0</math>, <math>x \ne 1</math>, <ma...")
- 11:43, 13 December 2023 (diff | hist) . . (-5) . . 1985 OIM Problems/Problem 6 (→Problem)
- 11:42, 13 December 2023 (diff | hist) . . (+2) . . 1985 OIM Problems/Problem 6
- 11:42, 13 December 2023 (diff | hist) . . (+492) . . N 1985 OIM Problems/Problem 6 (Created page with "== Problem == Given triangle <math>ABC</math>, we consider the points <math>D</math>, <math>E</math>, and <math>F</math> of lines <math>BC</math>, <math>AC</math>, and <math>A...")
- 11:39, 13 December 2023 (diff | hist) . . (+357) . . N 1985 OIM Problems/Problem 5 (Created page with "== Problem == To each positive integer <math>n</math> we assign an integer non-negative <math>f(n)</math> such that these conditions are satisfied: (i) <math>f(rs)=f(r)+f(s)<...")
- 11:36, 13 December 2023 (diff | hist) . . (+230) . . N 1985 OIM Problems/Problem 4 (Created page with "== Problem == If <math>x \ne 1</math>, <math>y \ne 1</math>, <math>x \ne y</math>, and: <cmath>\frac{yz-x^2}{1-x}=\frac{xz-y^2}{1-y}</cmath> Prove that both fractions are equ...")
- 11:34, 13 December 2023 (diff | hist) . . (0) . . 1985 OIM Problems/Problem 3 (→Problem)
- 11:34, 13 December 2023 (diff | hist) . . (+4) . . 1985 OIM Problems/Problem 3
- 11:33, 13 December 2023 (diff | hist) . . (+2) . . 1985 OIM Problems/Problem 3
- 11:33, 13 December 2023 (diff | hist) . . (+305) . . N 1985 OIM Problems/Problem 3 (Created page with "== Problem == Find the roots <math>r_1</math>, <math>r_2</math>, <math>r_3</math>, and <math>r_4</math> of the equation: <cmath>4x^4-ax^3+bx^2-cs+5=0</cmath> knowing that the...")
- 11:30, 13 December 2023 (diff | hist) . . (+61) . . 1985 OIM Problems/Problem 2 (→Problem)
- 11:30, 13 December 2023 (diff | hist) . . (+1) . . 1985 OIM Problems/Problem 2 (→Problem)
- 11:30, 13 December 2023 (diff | hist) . . (-24) . . 1985 OIM Problems/Problem 2
- 11:29, 13 December 2023 (diff | hist) . . (+205) . . N 1985 OIM Problems/Problem 2 (Created page with "== Problem == Let <math>P</math> be a point in the interior of equilateral triangle <math>ABC</math> such that: <math></math>PA=5,\;PB=7,\;<math> and </math>\;PC=8<math></math...")
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