On some special systems of equations (Q767926)
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scientific article; zbMATH DE number 3120127
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On some special systems of equations |
scientific article; zbMATH DE number 3120127 |
Statements
On some special systems of equations (English)
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1956
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Let \(\text{GF}(q)\) be a finite field of \(q\) elements. The author considers the system of equations of the form \[ x_1^{k_1}=f(x_3, \dots, x_n),\quad x_2^{k_2}=g(x_3, \dots, x_n). \] In case \(f\) and \(g\) are homogeneous polynomials of degrees \(m_1\) and \(m_2\), \((m_1, k_1)=(m_2, k_2)=1\), then the total number of solutions is \(q^{n-2}\)
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Diophantine equations
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finite fields
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