How about this:
Write n in the form n=kpa, where p|k.
Then ϕ(kpa) = ϕ(k)ϕ(pa) = ϕ(k)pa-1(p-1) = kpa - 2
Rearrange:
pa-1(p(k-ϕ(k)) + ϕ(k)) = 2
Notice, k-ϕ(k) is a positive integer, so p(k-ϕ(k)) + ϕ(k) is a positive integer.
Letting (p(k-ϕ(k)) + ϕ(k))=j, we have
pa-1j = 2
If...