## 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

### Keywords:

prime ideal; sum of two units; cyclotomic field
Full Text:

### 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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.