If at least one solution can be determined for a given problem, a solution to that problem is said to exist. Frequently, mathematicians seek to prove the existence of solutions (by means of a so-called existence theorem) and then investigate their uniqueness (by means of a so-called uniqueness theorem).
If one solution is known to exist but it is not known how many total solutions may exist, it is common to say that there is known to be at least one solution.
