Abstract
Let [Formula: see text] be a Dirichlet character (mod [Formula: see text]) with conductor [Formula: see text]. In a quite recent paper Zhao and Cao deduced the identity [Formula: see text], which reduces to Menon’s identity if [Formula: see text] is the principal character (mod [Formula: see text]). We generalize the above identity by considering even functions (mod [Formula: see text]), and offer an alternative approach to prove. We also obtain certain related formulas concerning Ramanujan sums.
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