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2016 AIME I Problems/Problem 7

Revision as of 16:53, 4 March 2016 by Ohmcfifth (talk | contribs) (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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Problem

For integers $a$ and $b$ consider the complex number \[\frac{\sqrt{ab+2016}}{ab+100}-({\frac{\sqrt{|a+b|}}{ab+100}})i\]

Find the number of ordered pairs of integers $(a,b)$ such that this complex number is a real number.

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