Abstract
In this paper we introduce a method to find the sum of powers on arithmetic progressions by using Cauchy’s equation and obtain a general formula. Then we apply our results to show how to determine some other sums of powers and sums of products. Our results are more general than those in [9]. Finally we discuss the sum of powers on arithmetic progressions in commmutative rings with characteristic 2 and find ‘full polynomials’.
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Kannappan, P.L., Zhang, W. Finding Sum of Powers on Arithmetic Progressions with Application of Cauchy’s Equation. Results. Math. 42, 277–288 (2002). https://doi.org/10.1007/BF03322855
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DOI: https://doi.org/10.1007/BF03322855
Keywords
- additive function
- sum of powers of integers and on arithmetic progression
- sum of products
- commutative ring
- characteristic