(boing!) Cnoocy Mosque O'Witz

Started with:

(a^2)b+c = (d^2)(b+c)

rearranged to:

(a^2-d^2)(b+c) = c(a^2-1)

Decided c = 1 would make life easier:

(a^2-d^2)(b+1) = (a^2-1)

Wanted to make the leftmost factor simpler, so I set a = d+2 (based on your example):

(4d+4)(b+1) = d^2+4d+3
4(d+1)(b+1) = (d+1)(d+3)
4(b+1) = d+3
4b+1 = d

And we already know a in terms of d. There's probably a more general relationship I missed by making the assumptions c = 1 and a = d+2, but this is not the math I'm being paid to do. :)