Sums of exceptional units in finite commutative rings
Volume 188 / 2019
Acta Arithmetica 188 (2019), 317-324
MSC: Primary 11T30; Secondary 11T99.
DOI: 10.4064/aa170131-23-8
Published online: 18 March 2019
Abstract
For a finite commutative ring with identity, we obtain an exact formula for the number of ways to represent each element of R as the sum of two exceptional units. This generalizes to finite rings a recent result of J. W. Sander for the ring \mathbb Z_n of residue classes mod n. We also obtain a formula for the number of exceptional units in R, generalizing to finite rings a result of Harrington and Jones in \mathbb Z_n.
