A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which 2a - 2b divides na - nb for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements α1,..., αk and β in the ring of integers A of a number field for which ∑i=1k αiβai divides ∑i=1k αizai for any z ∈ A. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.
- Algebraic integers
- Exponential congruences
- Polynomials of several variables
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