A note on the products $((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ and $((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$
Gürel, Erhan
Mathematical Communications, Tome 21 (2016) no. 1, p. 109-114 / Harvested from Mathematical Communications
Text on Mathematical Communications
We prove that for any positive integer $m$ there exists a positive real number $N_m$ such that whenever the integer $n\geq N_m$ neither the product $P^{n}_{m}=((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ nor the product $Q^{n}_{m}=((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$ is a square.
Publié le : 2016-03-09
Classification:  Polynomial products; diophantine equations,  11A41; 11A51;11D45 
@article{mc1521,
     author = {G\"urel, Erhan},
     title = {A note on the products $((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ and $((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$},
     journal = {Mathematical Communications},
     volume = {21},
     number = {1},
     year = {2016},
     pages = { 109-114},
     language = {eng},
     url = {http://dml.mathdoc.fr/item/mc1521}
}

Gürel, Erhan. A note on the products $((m+1)^{2}+1)((m+2)^{2}+1)\hdots(n^{2}+1)$ and $((m+1)^{3}+1)((m+2)^{3}+1)\hdots(n^{3}+1)$. Mathematical Communications, Tome 21 (2016) no. 1, pp.  109-114. http://gdmltest.u-ga.fr/item/mc1521/