Monday, 10 November 2025

Exercise (3.1).1

Write down three sets of complete residues of the following moduli:

(a) 5 (b) 10 (c) 13


(a)

$\{0, 1, 2, 3, 4\}$

$\{5, 6, 7, 8, 9\}$

$\{10, 11, 12, 13, 14\}$


(b)

$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$

$\{10, 11, 12, 13, 14, 15, 16, 17, 18, 19\}$

$\{20, 21, 22, 23, 24, 25, 26, 27, 28, 29\}$


(c)

$\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}$

$\{13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 24, 25\}$

$\{26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 37, 37, 38\}$