This a preprint and has not been peer reviewed. Data may be preliminary.

Thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in order to prove new formulas about the cardinality of each group of problems and about the intersection of each one of these sets. This work uses logical considerations about the complexity of NP-Hard problems in order to provea theoremabout the complexity ofproblems that allows us to identify NP problems even if their algorithms have infinite time of execution. This work ends by proving that the set of NP-Problems is definitely bigger than the set of P-Problems. Hence, I invite all the readers to develop the results of this article and to present their opinions about the used considerations in this work.

Motivated by the appearance of my previous article about the light in the very useful Book titled the worldwide list of alternative theories and critics (edition 2023), I tried to propose this experiment that tries to trap light beams in a rotating environment. I presented also the related formulas in this work and I could even guess some recurrence relations if the trapped Light-Beam is reflected several times from the moving wall of mirrors. However, the work exposes a contradiction concerning the reflected light beams velocity vectors and this made us suspect the correctness of some formulas when dealing with moving mirrors. This proposed experiment is very interesting, but the most important are the remarks that can be made by observing the contradictions exposed in this article.

Thanks to my short studies about informatics, I present to you this mathematical proof that deals with the sets of P problems, NP-Complete problems and NP-Hard problems in order to prove new formulas about the cardinality of each group of problems and about the intersection of each one of these sets. This work ends with a theoremabout the complexity ofproblems that allows us to identify NP problems even if their algorithms have infinite time of execution. Hence, I invite all the readers to use and develop the formulas of this article and to present their opinions about them.

A useful result about the Zeros of Riemann’s Hypothesis and Landau Siegel zeros