I don't think there is much new about this problem compared to N7 from 2006 since the solution there automatically gives you that $n$ is determined by a congruence modulo $b\varphi(b)<b^2$. Also, the generlization from $a=2$ to general $a$ is straightforward (and was even mentioned in the ISL thread).

Tintarn wrote: I don't think there is much new about this problem compared to N7 from 2006 since the solution there automatically gives you that $n$ is determined by a congruence modulo $b\varphi(b)<b^2$. Also, the generlization from $a=2$ to general $a$ is straightforward (and was even mentioned in the ISL thread). Yeah, that's true. Still, I posted the problem as it was just slightly different.