User contributions
- 12:34, 20 October 2013 (diff | hist) . . (+149) . . N 1975 IMO Problems/Problem 6 (Created page with "Find all polynomials P; in two variables, with the following properties: (i) for a positive integer n and all real t, x, y P(tx, ty)=(t^n)P(x, y)")
- 12:31, 20 October 2013 (diff | hist) . . (+181) . . N 1975 IMO Problems/Problem 5 (Created page with "Determine, with proof, whether or not one can find 1975 points on the circumference of a circle with unit radius such that the distance between any two of them is a rational number.")
- 12:31, 20 October 2013 (diff | hist) . . (-181) . . 1974 IMO Problems/Problem 5 (Blanked the page)
- 12:30, 20 October 2013 (diff | hist) . . (+181) . . N 1974 IMO Problems/Problem 5 (Created page with "Determine, with proof, whether or not one can find 1975 points on the circumference of a circle with unit radius such that the distance between any two of them is a rational number.")
- 12:28, 20 October 2013 (diff | hist) . . (+185) . . N 1975 IMO Problems/Problem 3 (Created page with "On the sides of an arbitrary triangle ABC; triangles ABR;BCP;CAQ are constructed externally with CBP = CAQ = 45°; BCP = ACQ = 30°; ABR = BAR = 15°: Prove that QRP = 90° and Q...")
- 12:23, 20 October 2013 (diff | hist) . . (+180) . . N 1974 IMO Problems/Problem 2 (Created page with "In the triangle ABC; prove that there is a point D on side AB such that CD is the geometric mean of AD and DB if and only if sin A sin B is less than or equal to sin²(C/2)")
- 12:12, 20 October 2013 (diff | hist) . . (+350) . . N 1973 IMO Problems/Problem 4 (Created page with "A soldier needs to check on the presence of mines in a region having the shape of an equilateral triangle. The radius of action of his detector is equal to half the altitude of t...")
- 12:09, 20 October 2013 (diff | hist) . . (+245) . . N 1973 IMO Problems/Problem 2 (Created page with "Determine whether or not there exists a finite set M of points in space not lying in the same plane such that, for any two points A and B of M; one can select two other points C ...")
- 12:05, 20 October 2013 (diff | hist) . . (+260) . . N 1972 IMO Problems/Problem 5 (Created page with "Let f and g be real-valued functions defined for all real values of x and y; and satisfying the equation f(x+y)+f(x-y)=2f(x)g(y) for all x, y. Prove that if f(x) is not i...")
- 12:01, 20 October 2013 (diff | hist) . . (+111) . . N 1972 IMO Problems/Problem 6 (Created page with "Given four distinct parallel planes, prove that there exists a regular tetrahedron with a vertex on each plane.")
- 12:00, 20 October 2013 (diff | hist) . . (+110) . . N 1972 IMO Problems/Problem 3 (Created page with "Let m and n be arbitrary non-negative integers. Prove that ((2m)!(2n)!)/mn!(m+n)! is an integer. (0! = 1.)")
- 11:54, 20 October 2013 (diff | hist) . . (+208) . . N 1972 IMO Problems/Problem 2 (Created page with "Prove that if n > 3; every quadrilateral that can be inscribed in a circle can be dissected into n quadrilaterals each of which is inscribable in a circle. '''SOLUTION''' ...")
- 11:40, 20 October 2013 (diff | hist) . . (+142) . . N 1971 IMO Problems/Problem 3 (Created page with "Prove that the set of integers of the form 2^k - 3(k = 2; 3; ...) contains an infinite subset in which every two members are relatively prime.")
- 11:37, 20 October 2013 (diff | hist) . . (+590) . . N 1971 IMO Problems/Problem 4 (Created page with "All the faces of tetrahedron ABCD are acute-angled triangles. We consider all closed polygonal paths of the form XY ZTX defined as follows: X is a point on edge AB distinct from ...")
- 11:25, 20 October 2013 (diff | hist) . . (+207) . . N 1971 IMO Problems/Problem 5 (Created page with "Prove that for every natural number m; there exists a finite set S of points in a plane with the following property: For every point A in S; there are exactly m points in S which...")
- 11:06, 20 October 2013 (diff | hist) . . (-11) . . 1969 IMO Problems/Problem 5
- 11:06, 20 October 2013 (diff | hist) . . (+181) . . N 1969 IMO Problems/Problem 5 (Created page with "Given n > 4 points in the plane such that no three are collinear. Prove that there are at least ³ n-3 ---- 2 ´ convex quadrilaterals whose vertices are four of the given points.")
- 11:04, 20 October 2013 (diff | hist) . . (+201) . . N 1969 IMO Problems/Problem 3 (Created page with "For each value of k = 1; 2; 3; 4; 5; find necessary and sufficient conditions on the number a > 0 so that there exists a tetrahedron with k edges of length a; and the remaining 6...")
- 10:56, 20 October 2013 (diff | hist) . . (-13) . . 1967 IMO Problems/Problem 2
- 10:42, 20 October 2013 (diff | hist) . . (+357) . . N 1967 IMO Problems/Problem 4 (Created page with "Let A0B0C0 and A1B1C1 be any two acute-angled triangles. Consider all triangles ABC that are similar to ¢A1B1C1 (so that vertices A1;B1;C1 correspond to vertices A;B;C; respecti...")
- 10:37, 20 October 2013 (diff | hist) . . (+393) . . N 1967 IMO Problems/Problem 6 (Created page with "In a sports contest, there were m medals awarded on n successive days (n > 1). On the first day, one medal and 1/7 of the remaining m - 1 medals were awarded. On the second day, ...")
- 10:34, 20 October 2013 (diff | hist) . . (+115) . . N 1967 IMO Problems/Problem 2 (Created page with "Prove that if one and only one edge of a tetrahedron is greater than 1; then its volume is <nowiki>·</nowiki> 1=8:")
- 08:22, 20 October 2013 (diff | hist) . . (-2) . . 1962 IMO Problems/Problem 5 (→Problem)
- 14:58, 19 October 2013 (diff | hist) . . (+2) . . 1962 IMO Problems/Problem 5 (→Solution)
- 14:57, 19 October 2013 (diff | hist) . . (+4) . . 1962 IMO Problems/Problem 5 (→Solution)
- 14:56, 19 October 2013 (diff | hist) . . (+8) . . 1962 IMO Problems/Problem 5 (→Solution)
- 14:55, 19 October 2013 (diff | hist) . . (+1,038) . . 1962 IMO Problems/Problem 5
