question on qfbsolve(Qfb(1,0,1),[N,F],3) call

Hello:

I am trying to use this form of the qfbsolve command:

qfbsolve(Qfb(1,0,1), [ N, F ], 3) which is shown in the user's guide as 
an example near the end of the description page.

Yes, I am aware that the normal use is qfbsolve(Q,n,{flag=0})

I did some C code programming using the gp2c-run -g command and found 
that I actually can get a 5% speed up using the [N,F] instead of the 
normal n entry in the qfbsolve() call for the range of numbers I am using.

Here's my question.

Suppose I have

    b = 741336
    c = 362900

    How can I successfully merge the factor matrices for b and c into 
the final factor matrix for (2*b^2*c^2)^2 or 4*b^4*c^4 ? and input both 
N = 4*b^4*c^4 and F into the qfbsolve call?

    The naive way is to do F = factor(4*b^4*c^4), but c is used once in 
my loop and b runs from c to 10x c . I would like to avoid the overhead 
if possible and found that there was a definite speed up.

In my real work I am using b,c around 10e5 to 10e6 size at the moment, 
they could get larger (10e6 to 10e7 in size)

Or should I just go N = 4*b*b*b*b*c*c*c*c ; F = factor(N) then call 
qfbsolve(Qfb(1,0,1),[N,F],3) ???

Randall