J Math Chem DOI 10.1007/s10910-017-0766-4 ORIGINAL PAPER Refinement of a generalized Fermat’s last theorem conjecture in natural vector spaces Ramon Carbó-Dorca 1 · Camelia Muñoz-Caro 2 · Alfonso Niño 2 · Sebastián Reyes 2 Received: 20 February 2017 / Accepted: 10 June 2017 © Springer International Publishing AG 2017 Abstract This study, at the light of a systematic computational search, provides a refined generalized Fermat’s last theorem conjecture with respect to the one, which appeared in a recent paper in this journal dealing with a Fermat-like behavior, attached in turn to the Minkowski norms defined within natural vector spaces. The aim of this kind of studies is to connect vector spaces with Boolean Hypercubes. This pretends also uncover the inner structure of vector sets, which appear important for the vectorial description of molecular structures and in this manner lead to new QSPR develop- ments. Keywords Natural vector semispaces · Inward vector powers · Complete vector sums · Minkowski norms · Fermat’s last theorem · Fermat and meta-Fermat natural vectors B Ramon Carbó-Dorca ramoncarbodorca@gmail.com Camelia Muñoz-Caro camelia.munoz@uclm.es Alfonso Niño alfonso.nino@uclm.es Sebastián Reyes sebastian.reyes@uclm.es 1 Secció de Química Quàntica i Matemàtica, Centre Europeu de Recerca Teòrica, Universitat de Girona, Campus de Montilivi, 17003 Girona, Catalonia, Spain 2 SciCom Research Group, Escuela Superior de Informática, Universidad de Castilla-La Mancha, Paseo de la Universidad 4, 13004 Ciudad Real, Spain 123