Abstract
We have already met with examples of finite fields, namely, the fields ℤ/pℤ, where p is a prime number. In this chapter we shall prove that there are many more finite fields and shall investigate their properties. This theory is beautiful and interesting in itself and, moreover, is a very useful tool in number-theoretic investigations. As an illustration of the latter point, we shall supply yet another proof of the law of quadratic reciprocity. Other applications will come later.
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Notes
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A. Hausner. On the law of quadratic reciprocity. Archiv der Math., 12 (1961), 182–183.
L. Holzer. Zahlentheorie. Leipzig: Teubner Verlagsgesellschaft, 1958.
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© 1982 Springer Science+Business Media New York
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Ireland, K., Rosen, M. (1982). Finite Fields. In: A Classical Introduction to Modern Number Theory. Graduate Texts in Mathematics, vol 84. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-1779-2_7
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DOI: https://doi.org/10.1007/978-1-4757-1779-2_7
Publisher Name: Springer, New York, NY
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