Difference between revisions of "1973 IMO Shortlist Problems/Cuba 2"
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Revision as of 22:17, 15 August 2006
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.
Resources
- 1973 IMO Shortlist Problems
- http://www.artofproblemsolving.com/Forum/viewtopic.php?p=603067 Discussion on AoPS/MathLinks]