1976 IMO Problems
Problems of the 18th IMO 1976 in Austria.
Contents
[hide]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 .