1973 IMO Shortlist Problems/Cuba 2
Problem
Decompose the polynomial
into polynomials of second degree with real coefficients.
Solution
We use the quadratic formula to find that the polynomial is zero when
,
which clearly occurs when , for all integral .
Hence
Q.E.D.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.