Exercise 3.4.3
I'll let you assume that s = 1 + 2 + 3 + ... + (p - 2) + (p - 1) =
(1/2)(p - 1)(p). You certainly want to use Wilson's Theorem,
too!
The following has been added after the first submission.
One can check by direct computation that the result holds
for p = 2. For p not equal to 2, use the formula above to express
s as a multiple of p. Now, argue that both of the integer factors
making
up this new expression for s [be careful here how you identify the two
integer factors!] divide the difference (p -1)! - (p - 1). What
do these observations allow you to conclude?