0 1 2 3 4 5 6 62 62 7 3 3 8 9 2 8 n 362 2 3 3 1 8 1 9 1 21 2 3 6 6 2 21 3 3 8 4 n 2 2 n n 3 2 n 3 n 3 2 n 3 n 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 9 6 9 6 9 6 90 6 9 6 1 1 0 1 1 0 8 8 2 3 2 3 1 2 A 2 3 B C 3 2 3 2 3 2 3 2 3 2 3 3 5 3 13 2 3 5 8 2 3 2 3 3 2 5 3 3 2 D 9 3 13 2 3 A 1 6 2 3 D 2 3 2 3 2 3 4 A 1 E F F 11 6 6 1 1 8 8 1 6 5 5 F F 8 1 6 5 5 F F G 6 H 5 5 625 F 62F F 3 3 G 6 5 625 5 3 F 62F 3 F 65 9 9 G IG G F G G 3 J6 J G 2 2 J3 G 6 5 5 625 3 F 62F 3 G IG G F 9 G 6 1 G1 6 4 G1 51 F1 G 6 4 G 5 F K G 6 5 IC F LH G 6 5 1 1 1 1 1 1 1 F 1 1 1 1 G 6 5 1 1 1 1 1 1 F 1 1 1 1 1 1 1 1 G 6 5 1 1 1 1 1 1 1 F 1 1 1 1 1 1 1 1 1 G 6 5 1 1 1 1 1 1 1 4 1 1 5 5 1 1 1 1 1 G 1 4 1 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 M M M M N H 2 3 6 5 5 5 0 1 6 N H 2 3 F 7 N H 2 3 4 6 9 N H 2 3 F F F F2 3 2 3 2 3 M M M 6 9 MLCO J M 2 F F1 3 F F M 1 H 2 N H 2 3 3P H 2 4 A M 3P F 6 F 2 Q 7 3 H2 36 ab ac mod n n ab ac n a b c n b c b c mod n since a n 1 N H 2 3 N2 N2 3 3 2 N H 2 3 36 H2 36 G F 6 G H 2 3 6 G F4 G 6 1 G F 6 5 1 1 1 1 1 1 F 1 1 1 1 1 1 1 1 1 H 2 3 6 J6 H2 JQ 6 2 H 2J 3 6 8 H 2JQ 3 6 3 6 3 G F 6 G H 2 3 6 F G A J J F G F J6 4 F JQ 6 J F G F J 6 JQ 5 P JQ J G F G F 6 0 F 0 0 0 0 0 0 G F F 0 1 0 1 1 0 0 1 0 0 1 0 1 0 1 1 0 1 0 1 8 9 F 6 F F 6 1 1 1 1 8 4 9 F 6 F 6 1 F 1 1 1 G F 6 1 F 1 1 1 1 1 1 A 2 3 6 6 J J F 7 7 G F6 1 2 3 6 G F 6 0 3 6 F 0 0 0 0 0 0 2 83 6 2 328 3 8 86R 6R 86R 6R 2 83 6 8 D 8 8 8 8 8 D 8 5 6 2 328 3 8 4 Q 4 G G F 8 G G 5 D 6 2 3 8 F 8 G G F F N 4 8 F 1 1 1 1 1 G 6 G F 6 625 F 2 5 7G 5 P 1 G H 2 3 6 H 5 5 3 3 F F 2 F 62F 35 2F 7G F F P 1 3 3 F G F 8 G N 2 3 4 4 5 62 36 4 C 4 F 2 3 4 M M 2 3 M LCO 2 3 4 23 5 A 2 3 2 A 4 2 3 3 4 4 4 G G F 6G G F 6 F G F 1 1 1 1 F 4 G 6 GF 6G 6 F G F 9 2 J J G F G F3 G F 9 9 2 3 F G 6 Q G F 2 3 Q G F G F 2 3 2 3 8 4 2 3 H 4 G F I I 6 2I 3 G F 2 3 I I I 5 G 4 F 2 3 8 2 3 2 3 G 6 G F 6 S 7G 5 P 1 5 G H 2 3 6 4 7G F F P 1 F N A 2 3 6 J J F G F6 1 2 3 6 2 83 6 2 328 3 8 2 E 0 3 T 4 4 A A 6 F8 2 3 6 2 3 283 6 2 3F28 3 A A GF 2 3 B 6 F 6 9 A U GF 2 3 2 3 8 8 6 F8 F 6 9 GF 2 3 2 3 8 6 F8 F 6 9 GF 2 3 2 3 8 6 F8 F 6 9 GF 2 3 2 3 9 GF 2 3 8 6 F8 F 6 9 2 3 9 2 3
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