On a problem in algebraic number theory
Author:
- J. WójcikJWJ. Wójcik
- 1 February 1996
- journal article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 119 (2) , 191-200
Abstract
Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’Keywords
This publication has 6 references indexed in Scilit:
- On a problem in elementary number theoryMathematical Proceedings of the Cambridge Philosophical Society, 1992
- On the congruence $f(x^k) ≡ 0 mod q$, where q is a prime and f is a k-normal polynomialActa Arithmetica, 1982
- On the composite Lehmer numbers with prime indices, IIIColloquium Mathematicum, 1981
- Multiplicative Groups of FieldsProceedings of the London Mathematical Society, 1972
- Bericht über neuere Untersuchungen und Probleme aus der Theorie der algebraischen Zahlkörper1965
- Sur certaines hypothèses concernant les nombres premiersActa Arithmetica, 1958