Abstract
In this paper, we study the number of integer pair solutions to the equation $|F(x,y)| = 1$ where $F(x,y) \in \Z[x,y]$ is an irreducible (over $\Z$) binary form with degree $n \geq 3$ and exactly three nonzero summands. In particular, we improve Thomas' explicit upper bounds on the number of solutions to this equation (see [13]). For instance, when $n \geq 219$, we show that there are no more than 32 integer pair solutions to this equation when $n$ is odd and no more than 40 integer pair solutions to this equation when $n$ is even, an improvement on Thomas' work in [13], where he shows that there are no more than 38 such solutions when $n$ is odd and no more than 48 such solutions when $n$ is even.
Citation
Greg Knapp. "The number of solutions to the trinomial Thue equation." Funct. Approx. Comment. Math. 69 (2) 247 - 270, December 2023. https://doi.org/10.7169/facm/2093
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