A naïve discussion of Fermat’s last theorem conundrum is described. The present theorem’s proof is grounded on the well-known properties of sums of powers of the sine and cosine functions, the Minkowski norm definition, and some vector-specific structures.
References
[1]
Wiles, A. (1995) Modular Elliptic-Curves and Fermat’s Last Theorem. Annals of Mathematics, 141, 443-551. https://doi.org/10.2307/2118559
[2]
Carbó-Dorca, R. (2017) Natural Vector Spaces (Inward Power and Minkowski Norm of a Natural Vector, Natural Boolean Hypercubes) and Fermat’s Last Theorem. Journal of Mathematical Chemistry, 55, 914-940. https://doi.org/10.1007/s10910-016-0708-6
[3]
Carbó-Dorca, R., Muñoz-Caro, C., Niño, A. and Reyes, S. (2017) Refinement of a Generalized Fermat’s Last Theorem Conjecture in Natural Vector Spaces. Journal of Mathematical Chemistry, 55, 1869-1877. https://doi.org/10.1007/s10910-017-0766-4
[4]
Niño, A., Reyes, S. and Carbó-Dorca, R. (2021) An HPC Hybrid Parallel Approach to the Experimental Analysis of Fermat’s Theorem Extension to Arbitrary Dimensions on Heterogeneous Computer Systems. The Journal of Supercomputing, 77, 11328-11352. https://doi.org/10.1007/s11227-021-03727-2
[5]
Carbó-Dorca, R., Reyes, S. and Niño, A. (2021) Extension of Fermat’s Last Theorem in Minkowski Natural Spaces. Journal of Mathematical Chemistry, 59, 1851-1863. https://doi.org/10.1007/s10910-021-01267-x
[6]
Ossicini, A. (2022) On the Nature of Some Eulerʼs Double Equations Equivalent to Fermatʼs Last Theorem. Mathematics, 10, 4471-4483. https://doi.org/10.3390/math10234471
[7]
Klykov, S.P. (2023) Elementary Proofs for the Fermat Last Theorem in Z Using One Trick for a Restriction in ZP. Journal of Science and Arts, 23, 603-608. https://doi.org/10.46939/J.Sci.Arts-23.3-a03
[8]
Klykov, S.P. and Klykova, M. (2023) An Elementary Proof of Fermat’s Last Theorem. https://doi.org/10.13140/RG.2.2.19455.59044
[9]
Gilbert, J.B. (2023) A Proof of Fermat’s Last Theorem. https://doi.org/10.13140/RG.2.2.27051.82722
[10]
Castro, C. (2023) Finding Rational Points of Circles, Spheres, Hyper-Spheres via Stereographic Projection and Quantum Mechanics. https://doi.org/10.13140/RG.2.2.12030.36164
[11]
Carbó-Dorca, R. (1998) Fuzzy Sets and Boolean Tagged Sets, Vector Semispaces and Convex Sets, QSM and ASA Density Functions, Diagonal Vector Spaces and Quantum Chemistry. In: Carbó-Dorca, R. and Mezey, P.G., Eds., Advances in Molecular Similarity, Vol. 2, JAI Press, London, 43-72. https://doi.org/10.1016/S1873-9776(98)80008-4
[12]
Carbó-Dorca, R. (2002) Shell Partition and Metric Semispaces: Minkowski Norms, Root Scalar Products, Distances and Cosines of Arbitrary Order. Journal of Mathematical Chemistry, 32, 201-223. https://doi.org/10.1023/A:1021250527289
[13]
Bultinck, P. and Carbó-Dorca, R. (2004) A Mathematical Discussion on Density and Shape Functions, Vector Semispaces and Related Questions. Journal of Mathematical Chemistry, 36, 191-200. https://doi.org/10.1023/B:JOMC.0000038793.21806.65
[14]
Carbó-Dorca, R. (2008) Molecular Quantum Similarity Measures in Minkowski Metric Vector Semispaces. Journal of Mathematical Chemistry, 44, 628-636. https://doi.org/10.1007/s10910-008-9442-z
[15]
Carbó-Dorca, R. (2019) Role of the Structure of Boolean Hypercubes When Used as Vectors in Natural (Boolean) Vector Semispaces. Journal of Mathematical Chemistry, 57, 697-700. https://doi.org/10.1007/s10910-018-00997-9
[16]
Carbó-Dorca, R. (2018) Boolean Hypercubes and the Structure of Vector Spaces. Journal of Mathematical Sciences and Modelling, 1, 1-14. https://doi.org/10.33187/jmsm.413116
[17]
Carbó-Dorca, R. (2022) Shadows’ Hypercube, Vector Spaces, and Non-Linear Optimization of QSPR Procedures. Journal of Mathematical Chemistry, 60, 283-310. https://doi.org/10.1007/s10910-021-01301-y
[18]
Carbó-Dorca, R. and Chakraborty, T. (2021) Extended Minkowski Spaces, Zero Norms, and Minkowski Hypersurfaces. Journal of Mathematical Chemistry, 59, 1875-1879. https://doi.org/10.1007/s10910-021-01266-y
[19]
Carbó-Dorca, R. (2021) Generalized Scalar Products in Minkowski Metric Spaces. Journal of Mathematical Chemistry, 59, 1029-1045. https://doi.org/10.1007/s10910-021-01229-3
[20]
Weisstein, E.W. Trigonometric Power Formulas. From MathWorld: A Wolfram Web Resource. https://mathworld.wolfram.com/TrigonometricPowerFormulas.html
