An Introduction to Gausss Number Theory
If there are an even number of least positive residues mod of these numbers , then is a quadratic residue of.
If is odd , is a quadratic nonresidue. Gauss's lemma can therefore be stated as , where is the Legendre symbol. It was proved by Gauss as a step along the way to the quadratic reciprocity theorem Nagell Euclid's lemma states that for any two integers and , suppose.
Then if is relatively prime to , then divides. Encyclopaedia Britannica. II, p. I, pp.
Carl Friedrich Gauss
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Gauss and the prime number theorem
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Introduction to Number Theory
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Carl Friedrich Gauss
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