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Linear Diophantine Equations
What amounts of money can you make with only $5 and $7 bills? Can you make $23 with those 2 types of bills?
Excel in math and science
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Concept Quizzes
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by Brilliant Staff
Consider all ordered pairs of integers \((x,y)\) such that \[\frac{5}{x}+\frac{7}{y} = \frac{12}{xy}.\]
The smallest positive integer value of \(x\) in these ordered pairs is \(1,\) since \(x=y=1\) satisfies the equation. What is the second smallest positive integer value of \(x\) in these ordered pairs?
Excel in math and science
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by Brilliant Staff
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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by Brilliant Staff
Hint: Don't try to list all of the possibilities!
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
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including olympiad champions, researchers, and professionals.
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That seems reasonable.
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by Brilliant Staff
Excel in math and science
Master concepts by solving fun, challenging problems.
It's hard to learn from lectures and videos
Learn more effectively through short, conceptual quizzes.
Our wiki is made for math and science
Master advanced concepts through explanations,
examples, and problems from the community.
Used and loved by 4 million people
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including olympiad champions, researchers, and professionals.
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That seems reasonable.
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by Brilliant Staff