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

Source: Polish MO Finals 1972 p3

August 22, 2024
inequalitiesalgebrapolynomial

Problem Statement

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 }.
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