In general, UP vs NP is a completely different problem than P vs. NP. In particular, while a strong connection of NP and (promise) UP is already known, P is widely believed to be different than NP. We define a problem that we call General Quadratic Congruences. We show General Quadratic Congruences is an NP-complete problem. Moreover, we prove General Quadratic Congruences is also in UP. In this way, we demonstrate that UP = NP.
https://hal.archives-ouvertes.fr/hal-01304025v6/document

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