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 23:30, 28 March 2007
Problem
For certain ordered pairs of real numbers, the system of equations
![$ax+by=1\,$](http://latex.artofproblemsolving.com/9/4/b/94b5a3e0b1a726c775259827de5d37bb20d31b62.png)
![$x^2+y^2=50\,$](http://latex.artofproblemsolving.com/d/5/b/d5b1e8d558c3818bdd87c0b06261db4f6a0977fe.png)
has at least one solution, and each solution is an ordered pair of integers. How many such ordered pairs
are there?
Solution
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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 |