2020/02/12 by Mesnager, Sihem, Kim, Kwang Ho, Choe, Jong Hyok +1
#FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2002.04912
Let l and k be two integers such that l|k. Define Tlk(X):=X+Xpl+⋯+X^pl(k/l-2)+X^pl(k/l-1) and Slk(X):=X-Xpl+⋯+(-1)(k/l-1)X^pl(k/l-1), where p is any prime. This paper gives explicit representations of all solutions in \GFpn to the affine equations Tlk(X)=a and Slk(X)=a, a∈ \GFpn. For the case p=2 that was solved very recently in \citeMKCL2019, the result of this paper reveals another solution.