Re: Factorial flight of fancy
- --- In email@example.com, Phil Carmody <thefatphil@...>
[Stuff - just see: http://tech.groups.yahoo.com/group/primenumbers/
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!