Difference between revisions of "1980 AHSME Problems/Problem 28"
(→Solution) |
m (→Solution) |
||
Line 21: | Line 21: | ||
+....</math> | +....</math> | ||
− | Therefore, the left term from <math>x^2n is x^(2n-3u)</math> | + | Therefore, the left term from <math>x^2n</math> is <math>x^(2n-3u)</math> |
− | the left term from <math>x^n is x^(n-3v)</math>, | + | the left term from <math>x^n</math> is <math>x^{(n-3v)}</math>, |
If divisible by h(x), we need 2n-3u=1 and n-3v=2 or | If divisible by h(x), we need 2n-3u=1 and n-3v=2 or |
Revision as of 12:58, 19 June 2021
Problem
The polynomial is not divisible by if equals
Solution
Assume
Therefore, the left term from is
the left term from is ,
If divisible by h(x), we need 2n-3u=1 and n-3v=2 or
2n-3u=2 and n-3v=1
The solution will be n=1/2 mod(3). Therefore n=21 is impossible
~~Wei
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 27 |
Followed by Problem 29 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.