Question

6. Compute the order of each element in (Z/8Z)* and in (Z/11Z)*.

Answer 1

" (3/82]* Result: If (din) . d divide If (dlnl . d divides a then nog en of orden din Flo72. E dild) divide 8 488 Here I 2.488 divia so no. of element of order 2014 2/8 = no. of element of order ? order 2 in H/82) $(2)= 1 4182 noi q element of order a a order uin (71182) b . : 014) = $12°) - 222 4-2 - 2 a no g. element g order 2 in 7/87 = 2 8lq si noi a element of orden j in Kloze $(8)= (22) to = 8-4-4 nog element of order 8 in Hlaze ay

so Zi187 hay a element of order 1 d element of order 2 2 element of order 4 4 & element of ordes 8 ents (7120) tlus f Zuz has 11/01 element of ander I is & ( 12) I f the 11 in so, no q 21/10 element of andes (W2 1,- = 10 of order a of ander 11 I so 2112 was element 4 to element