Some examples related to the \(abc\)-conjecture for algebraic number fields. (English) Zbl 0971.11009
The author constructs a numerical method for obtaining identities related to the uniform \(abc\)-conjecture for algebraic number fields.
Reviewer: Richard A. Mollin (Calgary)
MSC:
| 11D04 | Linear Diophantine equations |
| 11A55 | Continued fractions |
| 11Y65 | Continued fraction calculations (number-theoretic aspects) |
Keywords:
norm Euclidean; quadratic field; continued fraction; identities; uniform \(abc\)-conjectureReferences:
| [1] | J. Browkin, The \(abc\)-conjecture, Preprint. · Zbl 0971.11010 |
| [2] | J. Browkin and J. Brzeziński, Some remarks on the \?\?\?-conjecture, Math. Comp. 62 (1994), no. 206, 931 – 939. · Zbl 0804.11006 |
| [3] | G. Cooke, A weakening of the euclidean property for integral domains and applications to algebraic number theory I, J. Reine Angew. Math. 282 (1976), 133-156. · Zbl 0328.13013 |
| [4] | A. Granville and H.M. Stark, Abc implies no “Siegel zeros”, Preprint. · Zbl 0967.11033 |
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