# Squarefree values of trinomial discriminants

@article{Boyd2014SquarefreeVO,
title={Squarefree values of trinomial discriminants},
author={David W. Boyd and Greg Martin and Mark Thom},
journal={Lms Journal of Computation and Mathematics},
year={2014},
volume={18},
pages={148-169}
}
• Published 20 February 2014
• Mathematics
• Lms Journal of Computation and Mathematics
The discriminant of a trinomial of the form x n x m 1 has the form n n (n m) n m m m if n and m are relatively prime. We investigate when these discriminants have nontrivial square factors. We explain various unlikely-seeming parametric families of square factors of these discriminant values: for example, whenn is congruent to 2 (mod 6) we have that ((n 2 n+1)=3) 2 always divides n n (n 1) n 1 . In addition, we discover many other square factors of these discriminants that do not t into these…

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