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On sums of two units. (English) Zbl 0829.11057

Let \(K\) be a normal tamely ramified algebraic number field of degree \(n\) over the rationals \(\mathbb{Q}\), and let \((p)\) be a prime ideal of the rational integers. The author shows that any nonzero element of \((p)\) is not a sum of two units from the \(p\)-th cyclotomic field.

MSC:

11R27 Units and factorization
11R18 Cyclotomic extensions
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References:

[1] M. Newman, Diophantine Equations In Cyclotomic Fields, J. reine angew. Math.265 (1974), 84–89. · Zbl 0275.12008
[2] M. Newman, Consecutive Units, PAMS, V108, No 2 (1990), 303–306. · Zbl 0701.11055
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