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Difference between revisions of "AIME 2020(MOCK) Problems"

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Let <math>K</math> be a set of polynomials <math>P(x)</math> with integral coefficients such that the roots of <math>P(x)</math> are <math>cos \frac{\pi}{7}</math>, <math>cos \frac{\pi}{11}</math>, and <math>cos \frac{\pi}{17}</math>. What is the least possible sum of the coefficients of <math>P(x)</math>?
 
Let <math>K</math> be a set of polynomials <math>P(x)</math> with integral coefficients such that the roots of <math>P(x)</math> are <math>cos \frac{\pi}{7}</math>, <math>cos \frac{\pi}{11}</math>, and <math>cos \frac{\pi}{17}</math>. What is the least possible sum of the coefficients of <math>P(x)</math>?
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==Problem 3==

Revision as of 12:11, 11 June 2020

Problem 1

Let $N$ be $112123123412345... (1000 digits)$. What is the remainder when $N$ is divided by $21$?


Problem 2

Let $K$ be a set of polynomials $P(x)$ with integral coefficients such that the roots of $P(x)$ are $cos \frac{\pi}{7}$, $cos \frac{\pi}{11}$, and $cos \frac{\pi}{17}$. What is the least possible sum of the coefficients of $P(x)$?


Problem 3

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