!"#$# % & ' '$##( )*+ , -*& .(($//0(1. ("(2 3 4 *') 56 7& 62 3 62 3 8) . 9 :n, 8 -)) 2 362 3)) (2$31#8"# 1# "#9 :1#2"#21# 36#62"# 3(21#$ "#38'4 );.n.2n3 2n3& .2n n3 2n3n (2$3, 8 -n induces a natural partition of the integers into n classes: a and b are said to be in the same “residue class” or “congruence class” exactly when a n b.n (2$3, 8 -Define the residue class [i] to be the set of all integers that are congruent to i modulo n. 1.9:6<= $/$11/**>9#:6<= $$# 0**>9:6<= $ $#"**>9$/:6<= $/$11/**>90:6<= $$# 0**>9$#:6<= $ $#"**>?8 8 )*')2;3 2@(3& .;@?;.#/#/ #1#/')2;3 2@(3& .;@A).; (2;$3@( (2;$3B @(2;$3C )@(2;$3 ;@ ) .')2;3 23& .#3;5 53;$$13; ?8')(2;$3 (2$3& .#3(2;$ 5$33(2;$ D 9$:313(2;$3A))1.;$ 62;$3D 2$3(2;$3 (2$3 ) .+ '4 A .1EF/// 11#$F 6$"611 8 .+ @;) *+ * 8 16<#>5 F ) .#####5####F 8 16<#$#>5 F ) .$######$#$#$#$#5$###$###$#$#F& .G6<#= $#>H )5 F.5625 3F62F 3G6<#= $#>5625 3 F62F 35 F)GIG G.+ 65F.9:; G ; G9:;J G 2; 3 J6; 2
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