... uniform random number between 1 and N; where N is the number of elements in the array ...

Correction: several such random numbers. Alternatively, one random number 1..N, where N is the number of permutations.

The shuffle algorithm needs a random number sequence of finite length. A PRNG with 48 bits of internal state can generate at most 2⁴⁸ different sequences (of some particular length), because it is deterministic. If there are more permutations than that, some will never be selected.

Those using GNU/Linux can take a quick glimpse at the working of the standard shuffle tool, shuf.

$ strace -s0 -e open,read shuf -o /dev/null -i 1-17
...
open("/dev/urandom", O_RDONLY)          = 3
read(3, ""..., 11)                      = 11
...
$ strace -s0 -e open,read shuf -o /dev/null -i 1-1000
...
open("/dev/urandom", O_RDONLY)          = 3
read(3, ""..., 1250)                    = 1250
...

Here, in order to shuffle a list of integers 1-17, shuf actually wants 11 random bytes. For 1000 elements, shuf reads 1250 bytes of /dev/urandom.