Difference between revisions of "2022 AIME II Problems/Problem 13"
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There is a polynomial <math>P(x)</math> with integer coefficients such that<cmath>P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}</cmath>holds for every <math>0<x<1.</math> Find the coefficient of <math>x^{2022}</math> in <math>P(x)</math>. | There is a polynomial <math>P(x)</math> with integer coefficients such that<cmath>P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}</cmath>holds for every <math>0<x<1.</math> Find the coefficient of <math>x^{2022}</math> in <math>P(x)</math>. | ||
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==Solution== | ==Solution== | ||
Revision as of 07:28, 18 February 2022
Problem
There is a polynomial 
with integer coefficients such that![\[P(x)=\frac{(x^{2310}-1)^6}{(x^{105}-1)(x^{70}-1)(x^{42}-1)(x^{30}-1)}\]](http://latex.artofproblemsolving.com/0/f/e/0feb4850c1cb128a917f89180c0580e303c2c25f.png)
holds for every 
Find the coefficient of 
in .
Solution
See Also
| 2022 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 12 |
Followed by Problem 14 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
