A remark on a theorem of W. E. H. Berwick

Author:
Nicholas Tzanakis

Journal:
Math. Comp. **46** (1986), 623-625

MSC:
Primary 11R27; Secondary 11Y40

DOI:
https://doi.org/10.1090/S0025-5718-1986-0829633-6

MathSciNet review:
829633

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Abstract | References | Similar Articles | Additional Information

Abstract: We indicate and fill a gap in a theorem of W. E. H. Berwick concerning the computation of the fundamental units in a semireal biquadratic field.

**[1]**W. E. H. Berwick, "Algebraic number fields with two independent units,"*Proc. London Math. Soc.*, v. 34, 1932, pp. 360-378.**[2]**Andrew Bremner and Nicholas Tzanakis,*Integer points on 𝑦²=𝑥³-7𝑥+10*, Math. Comp.**41**(1983), no. 164, 731–741. MR**717717**, https://doi.org/10.1090/S0025-5718-1983-0717717-X**[3]**A. O. L. Atkin and B. J. Birch (eds.),*Computers in number theory*, Academic Press, London-New York, 1971. MR**0314733****[4]**Ray Steiner,*On the units in algebraic number fields*, Proceedings of the Sixth Manitoba Conference on Numerical Mathematics (Univ. Manitoba, Winnipeg, Man., 1976) Congress. Numer., XVIII, Utilitas Math., Winnipeg, Man., 1977, pp. 413–435. MR**532716****[5]**R. J. Stroeker,*On a diophantine equation of E. Bombieri: “Sulle soluzioni intere dell’equazione 4𝑥³=27𝑦²+𝑁” (Riv. Mat. Univ. Parma 8 (1957), 199–206)*, Nederl. Akad. Wetensch. Proc. Ser. A 80=Indag. Math.**39**(1977), no. 2, 131–139. MR**0437449****[6]**R. J. Stroeker,*On the Diophantine equation 𝑥³-𝐷𝑦²=1*, Nieuw Arch. Wisk. (3)**24**(1976), no. 3, 231–255. MR**0437448****[7]**Nicholas Tzanakis,*On the Diophantine equation 2𝑥³+1=𝑝𝑦²*, Manuscripta Math.**54**(1985), no. 1-2, 145–164. MR**808685**, https://doi.org/10.1007/BF01171704**[8]**Nikos Tzanakis,*On the Diophantine equation 𝑥²-𝐷𝑦⁴=𝑘*, Acta Arith.**46**(1986), no. 3, 257–269. MR**864261**, https://doi.org/10.4064/aa-46-3-257-269

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0829633-6

Article copyright:
© Copyright 1986
American Mathematical Society