pow:problem3s24
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| pow:problem3s24 [2024/03/10 20:44] – created mazur | pow:problem3s24 [2024/03/12 04:27] (current) – mazur | ||
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| + | <box 85% round orange|Problem 3 (due Monday, March 11) > | ||
| + | Let $p(x)=cx^n+c_1x^{n-1}+\ldots$ be a polynomial of degree $n$ with real coefficients and the leading | ||
| + | coefficient $c\neq 0$. Prove that at least one of the numbers $|p(0)|, |p(1)|, \ldots, |p(n)|$ | ||
| + | is greater or equal than $\displaystyle \frac{|c|n!}{2^n}$. Prove furthermore that this bound is best possible. | ||
| + | |||
| + | </ | ||
| + | We received a solution form Mithun Padinhare Veettil. | ||
| + | For a complete solution see the following link {{: | ||