IMO 1992 Shortlist
IMO 1992 Shortlist — 21 problems. 21 problems.
IMO 1992 Shortlist
21 problems · Source: IMO Compendium
Problems
| # | Origin | Problem |
|---|---|---|
| 1 | AUS | Prove that for any positive integer m there exist an infinite |
| 2 | CHN | Let R+ be the set of all nonnegative real numbers. Given two |
| 3 | CHN | The diagonals of a quadrilateral ABCD are perpendicular: |
| 4 | CHN | Given nine points in space, no four of which are coplanar, |
| 5 | COL | Let ABCD be a convex quadrilateral such that AC = |
| 6 | IND | Find all functions f : R \toR such that |
| 7 | IND | Circles G, G1, G2 are three circles related to each other as |
| 8 | IND | Show that in the plane there exists a convex polygon of 1992 |
| 9 | IRN | Let f(x) be a polynomial with rational coefficients and \alpha be |
| 10 | ITA | Let V be a finite subset of Euclidean space consisting of |
| 11 | JAP | In a triangle ABC, let D and E be the intersections of the bisec- |
| 12 | NET | Let f, g, and a be polynomials with real coefficients, f and g |
| 13 | NZL | Find all integer triples (p, q, r) such that 1 < p < q < r |
| 14 | POL | For any positive integer x define |
| 15 | PRK | Does there exist a set M with the following properties? |
| 16 | KOR | Prove that N = 5125−1 |
| 17 | SWE | Let \alpha(n) be the number of digits equal to one in the binary |
| 18 | USA | Let [x] denote the greatest integer less than or equal to x. |
| 19 | IRE | Let f(x) = x8 + 4x6 + 2x4 + 28x2 + 1. Let p > 3 be a prime |
| 20 | FRA | In the plane, let there be given a circle C, a line l tangent |
| 21 | GBR | For each positive integer n, denote by s(n) the greatest |