Order of an element Example: Z*: the multiplicative group modulo 7 7={1,2,34,5,6} order(1)=1 because 11 order(2)=3 because 23=8-1 and 3 is the smallest such number order(3)=6 because 36=93=23= 1 and 6 is order(4 )=3 because 43=64=1 and 6 is order(5)=6 because 56=253=43=1 and 6 is order(6)=2 because 6=36= 1 and 6 isOrder of an element Example: Z*7 : the multiplicative group modulo 7 Z*7 = {1,2,3,4,5,6} order(1) = 1 because 11 = 1 order(2) = 3 because 23 = 8 = 1 and 3 is the smallest such number order(3) = 6 because 36 = 93 = 23 = 1 and 6 is … order(4) = 3 because 43 = 64 = 1 and 6 is … order(5) = 6 because 56 = 253 = 43 = 1 and 6 is … order(6) = 2 because 62 = 36 = 1 and 6 is