Difference between revisions of "Non-residue"

Latest revision as of 22:23, 28 January 2020

of power $ n $ modulo $ m $

A number $ a $ for which the congruence $ x ^{n} \equiv a\ ( \mathop{\rm mod}\nolimits \ m) $ has no solution. See also Remainder of an integer.

Usually this term refers to the case $ n = 2 $. It was first used by C.F. Gauss in his Disquisitiones Arithmetica.

How to Cite This Entry:
Non-residue. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Non-residue&oldid=44366

@@ Line 1: / Line 1: @@
-''of power <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067270/n0672703.png" /> modulo <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067270/n0672704.png" />''
+{{TEX|done}}
-A number <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067270/n0672705.png" /> for which the [[Congruence|congruence]] <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067270/n0672706.png" /> has no solution. See also [[Remainder of an integer|Remainder of an integer]].
+''of power  $  n $
+modulo  $  m $''
+A number  $  a $
+for which the [[Congruence|congruence]]  $  x ^{n} \equiv a\ (  \mathop{\rm mod}\nolimits \  m) $
+has no solution. See also [[Remainder of an integer|Remainder of an integer]].
 ====Comments====
-Usually this term refers to the case <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/n/n067/n067270/n0672707.png" />. It was first used by C.F. Gauss in his Disquisitiones Arithmetica.
+Usually this term refers to the case  $  n = 2 $.
+It was first used by C.F. Gauss in his Disquisitiones Arithmetica.