On the Diophantine equation \(ax+by=n\) (Q2735378)
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scientific article; zbMATH DE number 1640374
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Diophantine equation \(ax+by=n\) |
scientific article; zbMATH DE number 1640374 |
Statements
16 January 2003
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binary linear Diophantine equation
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nonnegative integer solution
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solvability
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On the Diophantine equation \(ax+by=n\) (English)
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Let \(a,b\) be coprime positive integers. Let \(N(a,b)\) denote the number of positive integers \(n\) for which the equation \(ax+by=n\) has no nonnegative integer solution \((x,y)\). In the present paper the author proves the known fact that \(N(a,b)= (a-1)(b-1)/2\).
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