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math.NT2021
On power values of pyramidal numbers, II
Andrej Dujella, Kálmán Győry, Philippe Michaud-Jacobs +1
For , we define the th order pyramidal number by \[ \mathrm{Pyr}_m(x) = \frac{1}{6} x(x+1)((m-2)x+5-m). \] In a previous paper, written by the first-, second-, and fou…
math.NT2021★ 3 cited
Hermite equivalence of polynomials
Manjul Bhargava, Jan-Hendrik Evertse, Kálmán Győry +2
In this paper, we resurrect a long-forgotten notion of equivalence for univariate polynomials with integral coefficients introduced by Hermite in the 1850s. We show that the Hermit…