In this paper we propose to generalise a result of Loxton and Van der Poorten [1] in the following way. Let be an integer greater than or equal to two and be a finite subset of containing zero. will be said to be -free if, for all integers , the equality with forLet be the polynomial and the set of the -th roots of unity. We shall prove that is-free, when , if and only if, is bounded independently of .
@article{JTNB_1992__4_1_43_0, author = {Patrick Gonzalez}, title = {G\'en\'eralisation d'un r\'esultat de {Loxton} et van der {Poorten}}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {43--51}, publisher = {Universit\'e Bordeaux I}, volume = {4}, number = {1}, year = {1992}, doi = {10.5802/jtnb.63}, zbl = {0778.11015}, mrnumber = {1183917}, language = {fr}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.63/} }
TY - JOUR TI - Généralisation d'un résultat de Loxton et van der Poorten JO - Journal de Théorie des Nombres de Bordeaux PY - 1992 DA - 1992/// SP - 43 EP - 51 VL - 4 IS - 1 PB - Université Bordeaux I UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.63/ UR - https://zbmath.org/?q=an%3A0778.11015 UR - https://www.ams.org/mathscinet-getitem?mr=1183917 UR - https://doi.org/10.5802/jtnb.63 DO - 10.5802/jtnb.63 LA - fr ID - JTNB_1992__4_1_43_0 ER -
Patrick Gonzalez. Généralisation d'un résultat de Loxton et van der Poorten. Journal de Théorie des Nombres de Bordeaux, Volume 4 (1992) no. 1, pp. 43-51. doi : 10.5802/jtnb.63. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.63/