We show that the equation in the title (with $\Psi_m$ the $m$th cyclotomic polynomial) has no integer solution with $n \geq 1$ in the cases (m,p) = (15,41), (15,5581), (10,271). These equations arise in a recent group theoretical investigation by Akhlaghi, Khosravi and Khatami.
|Journal||Publicationes Mathematicae. Institutum Mathematicum Universitatis Debreceniensis|
|Publication status||Published - 2011|