Search vs decision
Show the following consequences of the hypothesis \mathsf{P} = \mathsf{NP}.
There is a polynomial-time algorithm that produces a satisfying assignment when given a satisfying Boolean formula.
Integers can be factored in polynomial time.
There is a polynomial-time algorithm that takes an undirected graph as input and finds a largest clique (see exercise 7.2) contained in that graph.
The algorithms you are asked to provide compute a function, but \mathsf{NP} contains languages, not functions. The \mathsf{P} = \mathsf{NP} assumption implies that deciding satisfiability, compositeness, and the existence of cliques of a given size is all solvable in polynomial time. But even though the assumption does not show how solutions are found, you must show that you can find them anyway.