Changes: Gauss' Number Theory Lemma

Latest revision as of 07:31, 18 February 2014

Gauss' number theory lemma is one of his lemmas which concerns number theory.

Statement

His number theory lemma states that if p is an odd prime, and a is coprime to p, in $a, 2a, 3a, 4a \dots, \frac{p-1}{2}a$ 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 $\left(\frac{a}{p}\right) = (-1)^n$ .

@@ Line 3: / Line 3: @@
 ==Statement==
-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>.
+His number theory 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:Number Theory]]
 [[Category:Lemma]]
-[[Category:Gauss]]