Difference between revisions of "1996 AIME Problems/Problem 8"
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== Problem == | == Problem == | ||
| + | The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers <math>(x,y)</math> with <math>x<y</math> is the harmonic mean of <math>x</math> and <math>y</math> equal to <math>6^{20}</math>? | ||
== Solution == | == Solution == | ||
Revision as of 14:59, 24 September 2007
Problem
The harmonic mean of two positive integers is the reciprocal of the arithmetic mean of their reciprocals. For how many ordered pairs of positive integers 
with 
is the harmonic mean of 
and 
equal to 
?
Solution
See also
| 1996 AIME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
