According to Cobham’s thesis, computational problems can be practically (or, in other words, feasibly) computed on some computational device only if they can be computed in polynomial time. Despite the presence of many objections to this claim, they are all not decisive. Then aga...
Open access
Research Article10.9734/JAMCS/2019/46241
This article is devoted to the lattice-theoretic analysis of Beal's conjecture. We discuss whether this conjecture is deducible from the laws of logic of divisibility.
Open access
Research Article10.9734/BJMCS/2017/33315
This short paper offers an example of possibly fruitful interactions between modal logic and number theory. In the paper, Conway's remark that p and p.2p + 1 can both be prime numbers is formulated as a formula of modal logic and then analyzed for its decidability.
Open access
Research Article10.9734/BJMCS/2016/27581
Assuming the conjecture that all effectively calculable functions must be Turing-machine computable, this paper demonstrates that the problem of recognizing Fibonacci numbers must be in general undecidable. This means that there is no algorithm, which in a finite number of steps...
Open access
Research Article10.9734/BJMCS/2015/19785
This short paper demonstrates a sketch of a generic algorithm that can generate integers written as the sum of N mth positive powers with any N≥2 and m≥1 in two different ways. As it is shown in the paper, such a generic algorithm is NP-hard. One can infer from this result that t...
Open access
Research Article10.9734/BJMCS/2015/17549
This short paper continues to discuss randomness of the Euler’s number e digits in decimal expansion. To analyze such randomness statistically, we exploit fixed-effects and random-effects Poisson panel-data models. The results of the regression models reveal the presence of some...
Open access
Research Article10.9734/BJMCS/2014/13537