pow:start
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pow:start [2026/01/27 01:51] mazur |
pow:start [2026/03/25 15:53] (current) mazur |
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| ====== Problem of the Week ====== | ====== Problem of the Week ====== | ||
| ~~NOTOC~~ | ~~NOTOC~~ | ||
| - | <box 85% round orange| Problem 1 (due Monday, February 9 ) > | + | <box 85% round orange| Problem 4 (due Monday, March 30 ) > |
| - | + | ||
| - | For which polynomials $f(x)$ the limit | + | |
| - | \[ \lim_{x\to \infty}\left(\sqrt[1013]{f(x+2)}-2\sqrt[1013]{f(x+1)}+\sqrt[1013]{f(x)}\right)\] | + | |
| - | is finite and non-zero? | + | |
| + | Let $n>0$ be an odd integer. Prove that there exists a set $S=\{A_1, \ldots, A_{2n}\}$ of $2n$ distinct points in the plane which are not collinear and such that if $i+j\neq 2n+1$ then the line $A_iA_j$ contains a third point from $S$. | ||
| </box> | </box> | ||
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| ===== Previous Problems and Solutions===== | ===== Previous Problems and Solutions===== | ||
| + | * [[pow:Problem3s26|Problem 3]] No solutions were submitted. | ||
| + | |||
| + | * [[pow:Problem2s26|Problem 2]] Solved by Prof. Emmett Wyman. | ||
| - | * [[pow:Problem1s26|Problem 1]] Solution | + | * [[pow:Problem1s26|Problem 1]] No solutions were submitted. |
| * [[pow:Fall 2025]] | * [[pow:Fall 2025]] | ||
pow/start.1769496688.txt · Last modified: 2026/01/27 01:51 by mazur