Equations in finite fields with restricted solution sets.: II (Algebraic equations)

Generalizing earlier results, it is shown that if A, B, C, D are "large" subsets of a finite field F-q, then the equations a + b = cd, resp. ab + 1 = cd can be solved with a is an element of A, b is an element of B, c is an element of C,d is an element of D. Other algebraic equations with solutions restricted to "large" subsets of F-q are also studied. The proofs are based on character sum estimates proved in Part I of the paper.