Could someone help me find the solutions to the following:
(x^2)+x=0 in Z5.
(x^2)+x=0 in Z6.
Thanks. MK
Hello, MK!
These are of the same type . . . I'll explain the first one.
x² + x .= .0 .(mod 5)
We can apply standard algebraic methods.
Factor: .x(x + 1) .= .0 .(mod 5)
Then: .x .= .0 .(mod 5) . → . x .= .5m, for some integer m.
And: .x+1 .= .0 .(mod 5) . → . x .= .5n - 1, for some integer n.