Difference between revisions of "1994 AIME Problems/Problem 7"
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== Problem == | == Problem == | ||
| + | For certain ordered pairs <math>(a,b)\,</math> of real numbers, the system of equations | ||
| + | <center><math>ax+by=1\,</math></center> | ||
| + | <center><math>x^2+y^2=50\,</math></center> | ||
| + | has at least one solution, and each solution is an ordered pair <math>(x,y)\,</math> of integers. How many such ordered pairs <math>(a,b)\,</math> are there? | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=1994|num-b=6|num-a=8}} | |
Revision as of 22:30, 28 March 2007
Problem
For certain ordered pairs 
of real numbers, the system of equations
has at least one solution, and each solution is an ordered pair 
of integers. How many such ordered pairs are there?
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 1994 AIME (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 | ||
