Abstract
Let f and g be nonconstant polynomials over a field K. In this paper we study the pairs (f, g) for which the intersection K[f] ∩ K[g] is larger than K. We describe all such pairs in case K has characteristic zero, as a consequence of classical results due to Ritt. For fields K of positive characteristic we present various results, examples, and algorithms.
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Beals, R.M., Wetherell, J.L. & Zieve, M.E. Polynomials with a common composite. Isr. J. Math. 174, 93–117 (2009). https://doi.org/10.1007/s11856-009-0105-y
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DOI: https://doi.org/10.1007/s11856-009-0105-y