1976 IMO Problems
Problems of the 18th IMO 1976 in Austria.
Contents
Day 1
Problem 1
In a convex quadrilateral (in the plane) with the area of the sum of two opposite sides and a diagonal is . Determine all the possible values that the other diagonal can have.
Problem 2
Let and for Prove that for any positive integer n the roots of the equation are all real and distinct.
Problem 3
A box whose shape is a parallelepiped can be completely filled with cubes of side If we put in it the maximum possible number of cubes, each of volume , with the sides parallel to those of the box, then exactly percent from the volume of the box is occupied. Determine the possible dimensions of the box.
Day 2
Problem 4
Find the largest number obtainable as the product of positive integers whose sum is .
Problem 5
Let a set of equations be given, with coefficients satisfying , , or for all , and . Prove that if , there exists a solution of this system such that all () are integers satisfying and for at least one value of .
Problem 6
For all positive integral , , , and . Prove that where is the integral part of .
- 1976 IMO
- IMO 1976 Problems on the Resources page
- IMO Problems and Solutions, with authors
- Mathematics competition resources
1976 IMO (Problems) • Resources | ||
Preceded by 1975 IMO |
1 • 2 • 3 • 4 • 5 • 6 | Followed by 1977 IMO |
All IMO Problems and Solutions |