let p be odd prime, and a,b be integers

1) prove that the congruence $\displaystyle {x}^{2}-ab\equiv (a-b)x(mod p)$ always have one solution

2) when does the above congruence have 2 solutions modulo p?

3) solve the congruence $\displaystyle 4{x}^{3}\equiv x(mod p) $