If q is the product of the set of small primes and c'=abq = qc, and d'd'+e' = c', and a must appear twice in the first a+1 [e',1,t] elements of [e',1], how do we know what factors will also make up the two values of t where a is a factor of [e',1,t]?
That is the question we're answering.
That is also the two values we are forcing with the grid.
This is the basis of the non-trivial Lookup.