Author:
Hajdu L.,Herendi O.,Tengely Sz.,Varga N.
Abstract
AbstractWe study the square values of Littlewood polynomials. Using various methods we give all these values for the degrees $$n=3, 5$$
n
=
3
,
5
and $$n\le 24$$
n
≤
24
even. Beside this, we gather computational data (by providing all solutions in a certain range) for n odd with $$n\le 17$$
n
≤
17
. We propose some striking problems for further research, as well.
Publisher
Springer Science and Business Media LLC
Reference34 articles.
1. Baker, A.: Bounds for the solutions of the hyperelliptic equation. Proc. Camb. Philos. Soc. 65, 439–444 (1969)
2. Balister, P., Bollobás, B., Morris, R., Sahasrabudhe, J., Tiba, M.: Flat Littlewood polynomials exist. Ann. Math. 19, 977–1004 (2020)
3. Bennett, M.A., Levin, A.: The Nagell–Ljunggren equation via Runge’s method. Monatsh. Math. 177, 15–31 (2015)
4. Beukers, F., Tengely, S.: An Implementation of Runge’s Method for Diophantine Equations. http://arxiv.org/abs/math.NT/0512418 (2005)
5. Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system. I. The user language. J. Symb. Comput. 24, 235–265 (1997)