Chapter 4 - Section 4.1 - Divisibility and Modular Arithmetic - Exercises - Page 244: 22

a) div = -2 mod = 87 b) div = -99 mod = 0 c) div = 10 mod = 309 d) div = 123 mod = 333

a) $ a = −111, m = 99$ \\ $a = m . ($a div m$) + ($a mod m$)$ $−111 = 99 . -2 + 87$ b) $ a = −9999, m = 101$ \\ $a = m . ($a div m$) + ($a mod m$)$ $−9999 = 101 . -99 + 0$ c) $ a = 10299, m = 999$ \\ $a = m . ($a div m$) + ($a mod m$)$ $10299 = 999 . 10 + 309$ d) $ a = 123456, m = 1001$ \\ $a = m . ($a div m$) + ($a mod m$)$ $123456 = 1001 . 123 + 333$