# zbMATH — the first resource for mathematics

The number of permutation binomials over $${\mathbb F}_{4p+1}$$ where $$p$$ and $$4p+1$$ are primes. (English) Zbl 1121.11077
Summary: We give a characterization of permutation polynomials over a finite field based on their coefficients, similar to Hermite’s Criterion. Then, we use this result to obtain a formula for the total number of monic permutation binomials of degree less than $$4p$$ over $${\mathbb F}_{4p+1}$$, where $$p$$ and $$4p+1$$ are primes, in terms of the numbers of three special types of permutation binomials. We also briefly discuss the case $$q=2p+1$$ with $$p$$ and $$q$$ primes.

##### MSC:
 11T06 Polynomials over finite fields
Full Text: