An HPC hybrid parallel approach to the experimental analysis of Fermat’s theorem extension to arbitrary dimensions on heterogeneous computer systems

Extension of Fermat’s last theorem in Minkowski natural spaces

“…Recent exhaustive supercomputations [6] in Minkowski's natural spaces of dimension (3 + 1) have shown a behavior similar to the vectors of the lesser dimension (2 + 1) . That is, empirical computational evidence allows to conjecture that the equation: holds.…”

“…However, obviously enough the computational time strongly increases as the value of the Hypercube dimension increases. In the computations presented in reference [6] and here, the maximal value of the hypercube dimension has been set to M = 15.…”

“…However, we can say that besides the supercomputing search, performed according to the reference [6], some tests have been achieved in i7 and i9 desktop computers, through Python code.…”

“…Three previous papers have been devoted to the problem of extending Fermat's last theorem. The initial one was almost purely theoretical [4] and was setting up the problem, the second paper was backed up with computational information [5] and constituted a new step into Fermat's theorem extension, and the third work recently published, presented an extended supercomputational framework to cope with the problem as far as possible [6].…”

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“…In references [2][3][4][5][6], one can consult several recent studies about Fermat's last theorem. Also, in our laboratory, several papers, see references [7][8][9][10], dealing with extending Fermat's theorem in larger dimensions, have been published. Even a recent publication consists of a simple demonstration of the original theorem [11].…”