For example, Zy = [[0],. [1), [2), [3), [417, [517, [61,). The element [5], represents the infinite set of integers of the form 5 plus an integer multiple of 7. That is [5]7 = [...-9, -2,5, 12, 19, 26,...} or, more formally, [5], = (y: y = 5 + 7q for some integer q ). Modular addition, [+], is defined on the set Z, in terms of integer addition as follows: [a] [+] [b]m equals the element of Zm that contains the integer a+b. Modular multiplication, [*], is defined on the set Z. in terms of integer multiplication as follows: [a] m ["] [bim equals the element of Z. that contains the integer ab. The set Z. with these operations is a ring for any integer m