Remember this is all mod p.
So
1 = p+1 = 2*p+1, etc.
In particular,
p-1 = -1
p-2 = -2, etc.
Try replacing each term on the left with 'something equal to it mod p' on the right.
Show that
(p-1)(p-2)...(p-r)==(-1)^r*r!(mod p)
for r=1, 2, ..., p-1.
I am totally lost on this one... Can you help me get started? Thanks.
Oops, this should have said Wilson's theorem in the title.