N_K, the set of positive integers that are sums of two units in O_K, is finite if K has no real quadratic subfield; explicit solutions are classified for cyclic or negative-discriminant cubic fields.
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Sums of two units in number fields
N_K, the set of positive integers that are sums of two units in O_K, is finite if K has no real quadratic subfield; explicit solutions are classified for cyclic or negative-discriminant cubic fields.