Can someone please help!?
In Z_7, give a reasonable interpretation for the expressions 1/2, -2/3, sqrt(-3), -1/6
Need help as soon as possible and would greatly appreciate it, thank you all!!
1/2 means
x times 2 = 1
In Z_7 what can you multiply by 2 to equal 1? Or in other words what number less than 7 can you multiply by 2 and get a remainder of 1 when you mod 7?
In Z_7
0x2 = 0
1x2 = 2
2x2= 4
3x2 = 6
4x2 = 1
5x2 = 3
6x2 = 5
So 1/2 would be 4 in Z_7
You can go about the other problems in a similar manor.
-2/3
well what is -2? it is the OPPOSITE of 2, meaning -2 + 2 = 0. So what number in Z_7 is does x + 2 = 0? well thats 5, and then what number times 3 equals 5? From the chart above, thats 6!
See if you can do the rest.