Let $p$ a prime odd number, $P\in (\mathbb Z/p\mathbb Z)[x]$ with $\text{deg}(P) Is it true if $a_{pā1}\neq 0$ then the polynomial function associed to $P$ is not a permutation of $\mathbb Z/p\mathbb Z$ ?
Polynomial and Permutation
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$\begingroup$
abstract-algebra
permutations
modular-arithmetic
recreational-mathematics
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0Here is a reference in 2 parts: (R. Lidl and G. L. Mullen. When does a polynomial over a finite field permute the elements of the field? The American Math. Monthly, 95(3), 243-246, 1988) (R. Lidl and G. L. Mullen. When does a polynomial over a finite field permute the elements of the field? II The American Math. Monthly, 100(1), 71-74, 1993). I wish you can reach them (I can't). ā 2017-01-25
1 Answers
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This question was asked and answered in sci.math many years ago. Here's a link: