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{\bf A. Masuda, D. Panario and Q. Wang}
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{\bf The Number of Permutation Binomials over ${\Bbb F}_{4p+1}$ where $p$ and $4p+1$ are Primes}
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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 ${\Bbb F}_{4p+1}$, 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.
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