Difference between revisions of "1990 AIME Problems/Problem 10"
m |
|||
| 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>C</math>? | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1990|num-b=9|num-a=11}} | |
Revision as of 01:33, 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 | ||
