• Corpus ID: 238857062

On the sum of the values of a polynomial at natural numbers which form a decreasing arithmetic progression

  title={On the sum of the values of a polynomial at natural numbers which form a decreasing arithmetic progression},
  author={Bakir Farhi},
The purpose of this paper consists to study the sums of the type P (n) + P (n − d) + P (n − 2d) + . . . , where P is a real polynomial, d is a positive integer and the sum stops at the value of P at the smallest natural number of the form (n − kd) (k ∈ N). Precisely, for a given d, we characterize the R-vector space Ed constituting of the real polynomials P for which the above sum is polynomial in n. The case d = 2 is studied in more details. In the last part of the paper, we approach the… 


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