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Nonexistence of permutation binomials of certain shapes. (English) Zbl 1162.11396
Summary: Suppose \(x^m+ax^n\) is a permutation polynomial over \({\mathbb F}_p\), where \(p>5\) is prime and \(m>n>0\) and \(a\in{\mathbb F}_p^*\). We prove that \(\gcd(m-n,p-1)\notin\{2,4\}\). In the special case that either \((p-1)/2\) or \((p-1)/4\) is prime, this was conjectured in a recent paper by A. Masuda, D. Panario and Q. Wang [Electron. J. Comb. 13, No. 1, Research paper R65, 15 p. (2006; Zbl 1121.11077)].

MSC:
11T06 Polynomials over finite fields
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