Summary
We prove that there is no algorithm to solve arbitrary polynomial equations over a field of rational functions in one letter with constants in a finite field of characteristic other than 2 and hence, Hilbert's Tenth Problem for any such field is undecidable.
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Oblatum 1-XI-1989
Supported in part by NSF Grant DMS 8605198.
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Pheidas, T. Hilbert's Tenth Problem for fields of rational functions over finite fields. Invent Math 103, 1–8 (1991). https://doi.org/10.1007/BF01239506
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DOI: https://doi.org/10.1007/BF01239506