19 citations · 53 across the 16 of their papers we have counts for
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math.NT2007
Nonexistence of permutation binomials of certain shapes
Ariane M. Masuda, Michael E. Zieve
Suppose x^m + c*x^n is a permutation polynomial over GF(p), where p>5 is prime, m>n>0, and c is in GF(p)^*. We prove that gcd(m-n,p-1) is not 2 or 4. In the special case that eithe…
math.NT2007★ 1 cited
Permutation binomials over finite fields
Ariane M. Masuda, Michael E. Zieve
We prove that if x^m + c*x^n permutes the prime field GF(p), where m>n>0 and c is in GF(p)^*, then gcd(m-n,p-1) > sqrt{p} - 1. Conversely, we prove that if q>=4 and m>n>0 are fixed…
math.NT2007
Rational functions with linear relations
Ariane M. Masuda, Michael E. Zieve
We find all polynomials f,g,h over a field K such that g and h are linear and f(g(x))=h(f(x)). We also solve the same problem for rational functions f,g,h, in case the field K is a…