10

Part of 1983 IMO Shortlist

Problems(1)

There exists an interval I

Source: IMO Longlist 1983, Problem 23

p

q

be integers. Show that there exists an interval

I

1/q

and a polynomial

P

with integral coefficients such that

\left|P(x)-\frac pq \right| < \frac{1}{q^2}

x \in I.

algebrapolynomialapproximationnumber theoryrational numberIMO Shortlist