document.write( "Question 350589: List all congruence classes module 7, with three elements in each. \n" ); document.write( "

Algebra.Com's Answer #250651 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
Congruence Classes Modulo 7:\r
\n" ); document.write( "\n" ); document.write( "[0] = {..., -7, 0, 7, ...}
\n" ); document.write( "[1] = {..., -6, 1, 8, ...}
\n" ); document.write( "[2] = {..., -5, 2, 9, ...}
\n" ); document.write( "[3] = {..., -4, 3, 10, ...}
\n" ); document.write( "[4] = {..., -3, 4, 11, ...}
\n" ); document.write( "[5] = {..., -2, 5, 12, ...}
\n" ); document.write( "[6] = {..., -1, 6, 13, ...}\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Note: Notice how [7] = {..., 0, 7, 14, ...} and that 0 and 7 are in [0]. It turns out that -7 is also in [7]. So basically this means that [0]=[7]. So we are done listing all the congruence classes (because any other class is equivalent to one of the classes shown above) \n" ); document.write( "

\n" );