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==Statement== |
==Statement== |
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| − | The lemma states that if p is an odd prime, and a is coprime to p, in <math>a, 2a, 3a, 4a \dots, \frac{p-1}{2}a</math> the least positive residues modulo is p. If n is the number of residues that are more than half of p, then <math>\left(\frac{a}{p}\right) = (-1)^n</math>. |
+ | The lemma states that if p is an odd prime, and a is coprime to p, in <math>a, 2a, 3a, 4a \dots, \frac{p-1}{2}a</math> the least positive residues modulo is p. If n is the number of residues (these will all be factors or p, obviously) that are more than half of p, then <math>\left(\frac{a}{p}\right) = (-1)^n</math>. |
[[Category:Carl Friedrich Gauss]] |
[[Category:Carl Friedrich Gauss]] |
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[[Category:Number Theory]] |
[[Category:Number Theory]] |
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Revision as of 05:58, 17 January 2014
Gauss' number theory lemma is one of his lemmas which concerns number theory.
Statement
The lemma states that if p is an odd prime, and a is coprime to p, in the least positive residues modulo is p. If n is the number of residues (these will all be factors or p, obviously) that are more than half of p, then .
