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LSpice
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It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Satz 3. Wenn das Polynom $f(X)$ (mit $g < n$) überhaupt eine Nullstelle hat, so ist die Anzahl aller (verschiedenen) Nullstellen von $f(X)$ mindestens $q^{n - g}$.

Apart from the references provided in other answers here, an excellent survey about Chevalley-WarningChevalley–Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Apart from the references provided in other answers here, an excellent survey about Chevalley-Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Satz 3. Wenn das Polynom $f(X)$ (mit $g < n$) überhaupt eine Nullstelle hat, so ist die Anzahl aller (verschiedenen) Nullstellen von $f(X)$ mindestens $q^{n - g}$.

Apart from the references provided in other answers here, an excellent survey about Chevalley–Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

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It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Apart from the references provided in other answers here, an excellent survey about Chevalley-Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Apart from the references provided in other answers here, an excellent survey about Chevalley-Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Apart from the references provided in other answers here, an excellent survey about Chevalley-Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

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Name
Name
  • 2k
  • 14
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It is worth to mention that in his original paper, E. Warning also findfinds a lower bound for the number of solutions:

enter image description here

Apart from the references provided byin other answers here, an excellent survey about Chevalley-WaringWarning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also find a lower bound for the number of solutions:

enter image description here

Apart from the references provided by other answers, an excellent survey about Chevalley-Waring theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

It is worth to mention that in his original paper, E. Warning also finds a lower bound for the number of solutions:

enter image description here

Apart from the references provided in other answers here, an excellent survey about Chevalley-Warning theorem, its history and applications and related problems about solving polynomial equations over finite fields, written by Jean-René Joly, is accessible from

Équations et variétés algébriques sur un corps fini (L'Enseignement Mathématique (1973))

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