pow:start
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pow:start [2024/03/10 16:43] mazur |
pow:start [2024/05/07 15:59] (current) mazur |
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| ====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
| ~~NOTOC~~ | ~~NOTOC~~ | ||
| - | <box 85% round orange|Problem 3 (due Monday, March 11) > | + | <box 85% round orange| > |
| - | Let $p(x)=cx^n+c_1x^{n-1}+\ldots$ be a polynomial of degree $n$ with real coefficients and the leading | + | The problem of the week will return in the Fall 2024 semester. We thank everyone who participated this Spring. For the Summer, we suggest reviewing problems from past semesters and working on the additional problems posted at the bottom of the provided solutions. |
| - | 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. | + | |
| </box> | </box> | ||
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| ===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
| + | * [[pow:Problem7s24|Problem 7]] Solved by Sasha Aksenchuk. | ||
| - | * [[pow:Problem2s24|Problem 2]] A solution submitted by | + | * [[pow:Problem6s24|Problem 6]] Solved by Sasha Aksenchuk. |
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| + | * [[pow:Problem5s24|Problem 5]] We did not receive any solutions. | ||
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| + | * [[pow:Problem4s24|Problem 4]] A solution submitted by Beatrice Antoinette. | ||
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| + | * [[pow:Problem3s24|Problem 3]] Solved by Mithun Padinhare Veettil. | ||
| * [[pow:Problem2s24|Problem 2]] A solution submitted by Sasha Aksenchuk. | * [[pow:Problem2s24|Problem 2]] A solution submitted by Sasha Aksenchuk. | ||
pow/start.1710103405.txt · Last modified: 2024/03/10 16:43 by mazur