IMO Shortlist 1983 problem 10


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2. travnja 2012.
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Let p and q be integers. Show that there exists an interval I of length 1/q and a polynomial P with integral coefficients such that
\left|P(x)-\frac pq \right| < \frac{1}{q^2}
for all x \in I.
Izvor: Međunarodna matematička olimpijada, shortlist 1983