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A class of exponential congruences in several variables
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Abstract
A problem raised by Selfridge and solved by Pomerance asks to ¯nd 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 1; : : : ; k and ¯ in the ring of integers A of a number ¯eld for which k Xi=1 i¯ai divides k Xi=1 izai for any z 2 A: Here we obtain a further generalization, proving the corresponding ¯niteness results in a multidimensional setting.
참고문헌 (6)
- "Proposed by H. Ruderman", pp.59~60 (1977)
- "409.A class of exponential congruences 735" (1915)
- "On primitive prime factors ofan bn", 58, pp.555~562 (1962)
- "Pairs where2a 2b divides na nb for alln", 93, pp.218~220 (1985)
- "Proposed by H. Ruderman", pp.288~289 (1976)
- "A ？niteness theorem for a class of exponentialcongruences", 127, pp.2225~2232 (1999)
관련 논문AI추천
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