Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Journal of Computing, Vol. 5, No 1, (2011), 1p-14p
Recently Garashuk and Lisonek evaluated Kloosterman sums
K (a) modulo 4 over a finite field F3m in the case of even K (a). They posed it as an open
problem to characterize elements a in F3m for which K (a) ≡ 1 (mod4) and K (a) ≡ 3 (mod4). In
this paper, we will give an answer to this problem. The result allows us to count the number of
elements a in F3m belonging to each of these two classes.