Sums of Reciprocals of Polynomials over Finite Fields
Kenneth H. Hicks, Xiang‐dong Hou, Gary L. Mullen · American Mathematical Monthly · 2012
We consider the sum of the reciprocals of all monic polynomials of a given degree over a finite field 픽q each raised to the power of k. When k ≤ q, the sum has a surprisingly simple result due to mysterious cancellations that occur in the sum. We discuss this interesting phenomenon and provide a new inductive proof.