MathDB

3

Part of 1972 Polish MO Finals

Problems(1)

|P(x) -1/2 | <1/1000, integer

Source: Polish MO Finals 1972 p3

8/22/2024
Prove that there is a polynomial P(x)P(x) with integer coefficients such that for all xx in the interval [110,910]\left[ \frac{1}{10} , \frac{9}{10}\right] we have ∣P(x)−12∣<11000.\left|P(x) -\frac12 \right| < \frac{ 1}{1000 }.
inequalitiesalgebrapolynomial