A CLASS OF EXPONENTIAL CONGRUENCES IN SEVERAL VARIABLES

Title & Authors
A CLASS OF EXPONENTIAL CONGRUENCES IN SEVERAL VARIABLES
Choi, Geum-Lan; Zaharescu, Alexandru;

Abstract
A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which $\small{2^a\;-\;2^b}$ divides $\small{n^a\;-\;n^b}$ for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements $\small{{\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}}$ in the ring of integers A of a number field for which $\small{{\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A}$. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.
Keywords
exponential congruences;algebraic integers;polynomials of several variables;
Language
English
Cited by
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