1. ## Finding solutions

Find all solutions of the equation x^3 = 2 (a) in Z_11; (b) in Z_13.

My lecturer isn't helpful and there are no examples in the notes given. Could you please help me with part (b). I should then be able to solve part (a).

Thanks

2. Originally Posted by charikaar
Find all solutions of the equation x^3 = 2 (a) in Z_11; (b) in Z_13.

My lecturer isn't helpful and there are no examples in the notes given. Could you please help me with part (b). I should then be able to solve part (a).

Thanks
Let's talk about a) for example.
$x^3 = 2$

There are only 11 possibilites:
$0^3 \equiv 0$

$1^3 \equiv 1$

$2^3 \equiv 8$

$3^3 \equiv 5$

$4^3 \equiv 8$

etc.

I get x = 7 as the only solution.

-Dan