A Menon-type identity in residually finite Dedekind domains

摘要

Let phi be the Euler's totient function and sigma k(n) = Sigma(d vertical bar n) d(k) that is, the sum of the kth powers of the divisors of n. B. Sury showed that Sigma gcd(t(1) - 1, t(2), . . . , t(r), n) = phi(n)sigma r-1(n) t(1) is an element of U(Z(n)), t(2), ... t(r) is an element of Z(n) where U(Z(n)) is the group of units in the ring of residual classes modulo n. Here, this identity is extended to residually finite Dedekind domains. (C) 2016 Elsevier Inc. All rights reserved.