Kannappan, Pl. Sum of powers of integers and the additive Cauchy equation. (English) Zbl 0988.39022 Soochow J. Math. 27, No. 1, 89-95 (2001). The author presents another variant of applying Cauchy’s functional equation to generate closed expressions for \(n\)-term sums of \(m\)-th powers of consecutive terms in an algebraic progression [cf. the reviewer, Aequationes Math. 21, 39-43 (1980; Zbl 0451.39006)], this time for \(n=4\), \(n=5\), the arithmetic progressions being \(1,2,\dots,n\) and \(1,3,5,\dots,2n-1\). A similar method is applied to sums of products. Reviewer: János Aczél (Waterloo/Ontario) Cited in 2 Documents MSC: 39B22 Functional equations for real functions 11B25 Arithmetic progressions Keywords:Cauchy’s functional equation; sum of powers on arithmetic progressions; sums of products Citations:Zbl 0451.39006 PDFBibTeX XMLCite \textit{Pl. Kannappan}, Soochow J. Math. 27, No. 1, 89--95 (2001; Zbl 0988.39022)