Difference between revisions of "2010 AMC 12B Problems/Problem 15"
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== Solution == | == Solution == | ||
| − | We have either <math>{i^{x}=(1+i)^{y}neqz}</math>, <math>{i^{x}= | + | We have either <math>{i^{x}=(1+i)^{y}\neqz}</math>, <math>{i^{x}=z\neq(1+i)^{y}}</math>, or <math>{(1+i)^{y}=z\neqi^x}</math>. |
== See also == | == See also == | ||
{{AMC12 box|year=2010|num-b=12|num-a=14|ab=B}} | {{AMC12 box|year=2010|num-b=12|num-a=14|ab=B}} | ||
Revision as of 14:11, 7 November 2010
Problem 15
For how many ordered triples 
of nonnegative integers less than 
are there exactly two distinct elements in the set 
, where 
?
Solution
We have either ${i^{x}=(1+i)^{y}\neqz}$ (Error compiling LaTeX. Unknown error_msg), 
, or ${(1+i)^{y}=z\neqi^x}$ (Error compiling LaTeX. Unknown error_msg).
See also
| 2010 AMC 12B (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 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
