1959 IMO Problems
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Problems of the 1st IMO 1959 Romania.
Contents
[hide]Day I
Problem 1
Prove that is irreducible for every natural number .
Problem 2
For what real values of is
given (a) , (b) , (c) , where only non-negative real numbers are admitted for square roots?
Problem 3
Let be real numbers. Consider the quadratic equation in :
Using the numbers , form a quadratic equation in , whose roots are the same as those of the original equation. Compare the equations in and for .