Question

The integers 5 and 15 are among a collection of 12 integers that form a group under multiplication modulo 56. list all 12.

Answer 1

☆☆ranshsangwan☆☆

solution:-

It must include 1 since that's the identity. 
5*15=19 so 19 is in the group. 
5*19=39 so that's in the group. 
5*39=27 
5*27=23 
5*23=3 
5*3=15 so that doesn't help! 
15*3=45 
45*5=1 so that doesn't help. 
5*5=25 
39*39=9 
39*3=5 which doesn't help. 
45*9=13 
So we have {1,3,5,9,13,15,19,23,25,27,39,45}.