217 citations
- University of OttawaCA3 papers
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- Bar-Ilan UniversityIL1 paper
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Showing 2007 · math.NTShow all
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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
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…
math.NT2007★ 47 cited
Intersections of polynomial orbits, and a dynamical Mordell-Lang conjecture
Dragos Ghioca, Thomas J. Tucker, Michael E. Zieve
We prove that if nonlinear complex polynomials of the same degree have orbits with infinite intersection, then the polynomials have a common iterate. We also prove a special case o…