Difference between revisions of "2000 AIME II Problems/Problem 6"
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== Problem == | == Problem == | ||
| + | For how many ordered pairs <math>(x,y)</math> of integers is it true that <math>0 < x < y < 10^{6}</math> and that the arithmetic mean of <math>x</math> and <math>y</math> is exactly <math>2</math> more than the geometric mean of <math>x</math> and <math>y</math>? | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2000|n=II|num-b=5|num-a=7}} | |
Revision as of 19:11, 11 November 2007
Problem
For how many ordered pairs 
of integers is it true that 
and that the arithmetic mean of 
and 
is exactly 
more than the geometric mean of and ?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2000 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
