Abstract
Given a commutative ring R with 1∈R and the multiplicative group R⁎ of units, an element u∈R⁎ is called an exceptional unit if 1−u∈R⁎, i.e., if there is a u′∈R⁎ such that u+u′=1. We study the case R=Zn:=Z/nZ of residue classes modn and determine the number of representations of an arbitrary element c∈Zn as the sum of two exceptional units. As a consequence, we obtain the sumset Zn⁎⁎+Zn⁎⁎ for all positive integers n, with Zn⁎⁎ denoting the set of exceptional units of Zn.
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