On representations of real quadratic integers as sums of unitary fractions

Résumé

We verify that each natural number $t>1$ can be expressed as a sum of unitary fractions of different natural numbers such that the least common multiple among them is coprime with a fixed value $v$. Using this fact, we characterize the real quadratic integers which appear in the representation of 1 as a unitary fraction sum over the real quadratic integer ring.