1976 IMO Problems
Problems of the 18th IMO 1976 in Austria.
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.
Let and for Prove that for any positive integer n the roots of the equation are all real and distinct.
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.
Find the largest number obtainable as the product of positive integers whose sum is .
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 .
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
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