Small Values at Integers

★ 7/10algebra Polynomials Lagrange Interpolation inequality

Problem

Let $f(x) = ax^2 + bx + c$ with $a > 0$ . Prove that there are at most two integers $s, t$ for which

|f(s)| < \frac{a}{2}, \qquad |f(t)| < \frac{a}{2}.

Answer

Solution

Difficulty	7/10
Topics	algebra, Polynomials, Lagrange Interpolation, inequality

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