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math.NT2025
On the structure of solutions graph of the Markoff-Hurwitz equation and recurrence sequences
Ilya V. Vyugin
We prove that almost all solutions of the Markoff-Hurwitz equation over a residue field modulo can be obtained from one another by a chain of natural transformations. We also s…
math.NT2020
Polynomial Equations in Subgroups and Applications
Sergei V. Konyagin, Igor E. Shparlinski, Ilya V. Vyugin
We obtain a new bound for the number of solutions to polynomial equations in cosets of multiplicative subgroups in finite fields, which generalises previous results of P. Corvaja a…