Maxim Vsemirnov

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The propositional satisfiability problem (SAT) is one of the most naturalNP-complete problems, and therefore its complexity is crucial for the computational complexity theory. Since SAT is NP-complete, it is unlikely that SAT can be solved in polynomial time. However, it is still important to understand how much time is required to solve SAT, even if this(More)
We find a new Fibonacci-like sequence of composite numbers and reduce the current record for the starting values to A0 = 106276436867 and A1 = 35256392432. In this note we consider Fibonacci-like sequences, i.e., the sequences {An} satisfying the recurrence relation An = An−1 + An−2, n ≥ 2. (1) Ronald Graham [1] proved that there exist relatively prime(More)
The classical Carmichael numbers are well known in number theory. These numbers were introduced independently by Korselt in [8] and Carmichael in [2] and since then they have been the subject of intensive study. The reader may find extensive but not exhaustive lists of references in [5, Sect. A13], [11, Ch. 2, Sec. IX]. Recall that a positive composite(More)