15.92 (2002)

A group $\langle x, y \mid x^l = y^m = (xy)^n = 1 \rangle$ is called the triangle group with parameters $(l, m, n)$. It is proved in (A. M. Brunner, R. G. Burns, J. Wiegold, Math. Scientist, 4 (1979), 93–98) that the triangle group $(2, 3, 30)$ has uncountably many non-isomorphic homomorphic images that are residually finite alternating groups. Is the same true for the triangle group $(2, 3, n)$ for all $n > 6$?