--- In

primenumbers@yahoogroups.com, Phil Carmody <thefatphil@...>

wrote:

[Stuff - just see:

http://tech.groups.yahoo.com/group/primenumbers/
message/18206?threaded=1&var=1&l=1 ]

On sci.math just now, Gerry Myerson has chipped in the following:

<<<

It's shown in Niven, Zuckerman, and Montgomery that if p is 1 mod 4

then ( (p - 1) / 2 ) factorial squared is -1 mod p (p. 54), and

it's an exercise to show that if p is 3 mod 4 then the quantity is

plus-or-minus 1 (exercise 2.1.18).

Maybe something interesting happens with ( (p - 1) / 3 ) factorial,

for those primes congruent 1 mod 3.

>>>

I instantaniously bought Niven, Zuckerman, and Montgomery (huge, not

petit), and unless anyone else wants to chip in with a review right

now, I shall do so when it arrives in a month or so.

G^HMerry unorthodox Christmas to me!

Phil