2016 AIME I Problems/Problem 7: Difference between revisions
Created page with "==Problem== For integers <math>a</math> and <math>b</math> consider the complex number <cmath>\frac{\sqrt{ab+2016}}{ab+100}-({\frac{\sqrt{|a+b|}}{ab+100}})i</cmath> Find the ..." |
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Find the number of ordered pairs of integers <math>(a,b)</math> such that this complex number is a real number. | Find the number of ordered pairs of integers <math>(a,b)</math> such that this complex number is a real number. | ||
== See also == | |||
{{AIME box|year=2016|n=I|num-b=6|num-a=8}} | |||
{{MAA Notice}} | |||
Revision as of 16:55, 4 March 2016
Problem
For integers 
and 
consider the complex number
![\[\frac{\sqrt{ab+2016}}{ab+100}-({\frac{\sqrt{|a+b|}}{ab+100}})i\]](http://latex.artofproblemsolving.com/9/4/a/94aed5cb77ab692adad418e0f67918ea8fe39dc6.png)
Find the number of ordered pairs of integers 
such that this complex number is a real number.
See also
| 2016 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
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