Difference between revisions of "Complete residue system"
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In other words, the set contains exactly one member of each residue class. | In other words, the set contains exactly one member of each residue class. | ||
==Examples== | ==Examples== | ||
| − | <math>\{1,2,3\}</math>, <math>\{4,5,6\}</math>, and <math>\{9,17,85\}</math> are all Complete residue systems <math>\pmod{3}</math> | + | <math>\{1,2,3\}</math>, <math>\{4,5,6\}</math>, and <math>\{9,17,85\}</math> are all Complete residue systems <math>\pmod{3}</math>. |
<math>\{k,k+1,k+2,k+3,\ldots,k+m-1\}</math> is a complete residue system <math>\pmod{m}</math>, for any integer <math>k</math> and positive integer <math>m</math>. Basically, any consecutive string of <math>m</math> integers forms a complete residue system <math>\pmod{m}</math>. | <math>\{k,k+1,k+2,k+3,\ldots,k+m-1\}</math> is a complete residue system <math>\pmod{m}</math>, for any integer <math>k</math> and positive integer <math>m</math>. Basically, any consecutive string of <math>m</math> integers forms a complete residue system <math>\pmod{m}</math>. | ||
Latest revision as of 19:53, 1 January 2010
A Complete residue system modulo 
is a set of integers which satisfy the following condition: Every integer is congruent to a unique member of the set modulo .
In other words, the set contains exactly one member of each residue class.
Examples
, 
, and 
are all Complete residue systems 
.
is a complete residue system 
, for any integer 
and positive integer 
. Basically, any consecutive string of integers forms a complete residue system .
