## 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

### Keywords:

finite field; permutation polynomial; binomials
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