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Sums of exceptional units in finite commutative rings

Volume 188 / 2019

C. Miguel Acta Arithmetica 188 (2019), 317-324 MSC: Primary 11T30; Secondary 11T99. DOI: 10.4064/aa170131-23-8 Published online: 18 March 2019


For a finite commutative ring $R$ 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 $\mathbb Z_n$.


  • C. MiguelInstituto de Telecomunicações
    Department of Mathematics
    Beira Interior University
    6201-001 Covilhã, Portugal

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