Difference between revisions of "1990 AIME Problems/Problem 10"
m |
m (→Problem) |
||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | The sets <math>\displaystyle A = \{z : z^{18} = 1\}</math> and <math>\displaystyle B = \{w : w^{48} = 1\}</math> are both sets of complex roots of unity. The set <math>C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}</math> is also a set of complex roots of unity. How many distinct elements are in <math> | + | The sets <math>\displaystyle A = \{z : z^{18} = 1\}</math> and <math>\displaystyle B = \{w : w^{48} = 1\}</math> are both sets of complex roots of unity. The set <math>C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}</math> is also a set of complex roots of unity. How many distinct elements are in <math>C_{}^{}</math>? |
== Solution == | == Solution == | ||
Revision as of 00:53, 2 March 2007
Problem
The sets 
and 
are both sets of complex roots of unity. The set 
is also a set of complex roots of unity. How many distinct elements are in 
?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1990 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 9 |
Followed by Problem 11 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
