Abstract:This paper studies single-cycle polynomials over the integer residue ring Z/(pn) with prime p≥5 and integer n≥2, and presents several classes of such single-cycle polynomials. As the research of single-cycle polynomials over Z/(pn) can be reduced to the case over Z/(p2), an exact characterization of single-cycle polynomials over Z/(5) is given in terms of their coefficients, and then a complete characterization of single-cycle polynomials of degree 6 over Z/(52) is given based on it. In addition, a partial construction of single-cycle polynomials of degree (p−1) over Z/(p2) is also proposed.
游伟, 戚文峰. 剩余类环Z/(pn)上若干类单圈多项式构造[J]. 电子与信息学报, 2012, 34(4): 802-806.
You Wei, Qi Wen-Feng. Construction of Several Classes of Single-cycle Polynomials over Z/(pn). , 2012, 34(4): 802-806.