P versus NP

P versus NP is considered as one of the most important open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? A precise statement of the P versus NP problem was introduced independently in 1971 by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is UP. Whether UP = NP is a fundamental question that it is as important as it is unresolved. To attack the P = NP question the concept of NP-completeness is very useful. Quadratic Congruences is a well-known NP-complete problem. We show Quadratic Congruences is in UP. Since UP is closed under reductions, then we obtain that UP = NP. If any single NP-complete problem is in P, then P = NP. We prove Quadratic Congruences is also in P. In this way, we demonstrate that P = NP.