Motohashi, Y. (ed.), Analytic number theory. Proceedings of the 39th Taniguchi international symposium on mathematics, Kyoto, Japan, May 13–17, 1996. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 247, 95-101 (1997).
where are positive integers with . It was conjectured independently by M. Hoffman [Pac. J. Math. 152, 275-290 (1992; Zbl 0763.11037)] and by C. Markett [J. Number Theory 48, 113-132 (1994; Zbl 0810.11047)] that
for positive integers with . This conjecture is proved in the present paper by generating functions arguments. The author then uses this result to derive formulas for certain double and triple sums (proved earlier by different methods).