MAD 4301 Midterm: MAS4301 S97 Test 2
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Instructions: do not write your answers on this paper, use separate answer sheets. Z/10. (3) in z/m, the congruence class [a] is a unit if and only if (a, m) = 1. (4) suppose a 6 0 (mod m). In z/m, the congruence class [a] is a zero divisor if and only if (a, m) > 1. (5) suppose m > 1, (c, m) = 1, and a is arbitrary. S = {a, a + c, a + 2c, a + 3c, . , a + (m 1) c} . Let f : s {0, 1, . , m 1} be the remainder function modulo m. that is, f (x) is the remainder upon division of x by m. show that f is one-to-one and onto.
