On the Galois group of \(x^ p+ax+a=0\) (Q810577)
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scientific article; zbMATH DE number 4214150
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Galois group of \(x^ p+ax+a=0\) |
scientific article; zbMATH DE number 4214150 |
Statements
On the Galois group of \(x^ p+ax+a=0\) (English)
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1991
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Let \(p>3\) be a prime and let a be an integer such that p \(\nmid a\) and \(f(x)=x^ p+ax+a\) is irreducible over \({\mathbb{Q}}\). It is proved that the Galois group of f(x) is the symmetric group \(S_ p\) unless \(p\equiv 1 mod 8\) and \((p-1)^{p-1}a+p^ p\) is a square.
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trinomial
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Galois group
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symmetric group
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