中文摘要：

设P是一个奇素数，q是P的方幂。aFq／{0,2,3,4,6}使得多项式x^2＋a＋aFq[x]为Fq上不可约多项式，证明映射φ：fq→Fq,x｜x^2＋ax＋a/x3-a-2/a^2（a-3）x-a-2/a^2（a-3）不是一一映射，从而证实了Kyureghan和Ozbudak在2012年提出的一个猜测。

英文摘要：

Let p be an odd prime number and q a power of p. Let a ∈ Fq ／{0,2,3,4,6} such that the polynomial x^2＋ax＋a ∈Fq[x]is irreducible over Fq.It is shown that the mapping φ：fq→Fq,x｜x^2＋ax＋a/x3-a-2/a^2（a-3）x-a-2/a^2（a-3）is not bijective, which confirms a conjecture of Kyureghan and Ozbudak in 2012.