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Warning’s second theorem with relaxed outputs. (English) Zbl 1440.11225

Summary: We present a generalization of E. Warning’s second theorem to polynomial systems over a finite local principal ring with restricted input and relaxed output variables [Abh. Math. Semin. Univ. Hamb. 11, 76–83 (1935; JFM 61.1043.02)]. This generalizes a recent result [the author et al., Combinatorica 37, No. 3, 397–417 (2017; Zbl 1399.11177)] (and gives a new proof of that result). Applications to additive group theory, graph theory and polynomial interpolation are pursued in detail.

MSC:

11T06 Polynomials over finite fields
11B75 Other combinatorial number theory
11D79 Congruences in many variables
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