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Permutation binomials. (English) Zbl 0702.11085
Author’s summary: A polynomial \(f\) over a finite field \(\mathbb F\) is a permutation polynomial if the mapping \(\mathbb F\to \mathbb F\) defined by \(f\) is one-to-one. We are concerned here with binomials, that is, polynomials of the shape \(f=aX^ i+bX^ j+c,\) \(i>j\geq 1\). Even in this restricted setting, it is impossible to give general necessary and sufficient conditions on \(a, b, c\) for \(f\) to be a permutation polynomial. We review, and systematize, what is known.
Reviewer: J.H.van Lint

MSC:
11T06 Polynomials over finite fields
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