Ongan, PinarGülmez Temür, BurcuTemur, Burcu GulmezGülmez Temür, BurcuMathematicsMathematicsMathematics2024-07-052024-07-0520200219-49881793-682910.1142/S021949882050067Xhttps://doi.org/10.1142/S021949882050067Xhttps://hdl.handle.net/20.500.14411/3148In this paper, we study polynomials of the form f(x) = x (qn-1/q-1+1) + bx is an element of F-qn[x], where n = 5 and list all permutation polynomials (PPs) and complete permutation polynomials (CPPs) of this form. This type of polynomials were studied by Bassalygo and Zinoviev for the cases n = 2 and n = 3, Wu, Li, Helleseth and Zhang for the case n = 4, p not equal 2, Bassalygo and Zinoviev answered the question for the case n = 4, p= 2 and finally by Bartoli et al. for the case n = 6. Here, we determine all PPs and CPPs for the case n = 5.eninfo:eu-repo/semantics/closedAccessPermutation polynomialsfinite fieldsArticleQ3194WOS:0005343704000073