[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj 4:44 amPahio, happy to say "Nick" of Mersenneforum.org has given a simple
proof.

[p] **Modified Fermat's theorem** by akdevaraj Jun 22Before replying to Pahio's call for proof would like to add that
I forgot to add the condition: a and p should be co-prime.

[p] **modidied Fermat's theorem** by pahio Jun 21Nice theorem! How do you prove it?

[p] **Modified Fermat's theorem** by akdevaraj Jun 21Modified Fermat's theorem: Let a belong to the ring of Gaussian integers
Then a^(p^2-1)= = 1 (mod p). Here p is a prime number with shape 4m+1 or 4m+3.

[p] **conjecture pertaining to Gaussian integers** by akdevaraj Apr 27Happy to report that "Nick", on mersenneforum.org, has stated
that my conjecture can be taken as proved.

[p] **conjecture pertaining to Gaussian integers** by akdevaraj Apr 27Happy to report that "Nick", on mersenneforum.org, has stated
that my conjecture can be taken as proved.

[p] **conjecture pertaining to Gaussian integers** by akdevaraj Apr 26A couple of examples given below:Reading GPRC: gprc.txt ...Done.
GP/PARI CALCULATOR Version 2.6.1 (alpha)
i686 running mingw (ix86/GMP-5.0.1 kernel) 32-bit version
compiled: Sep 20 2013, gcc version 4.6.3 (GCC)
(readline v6.2 enabled, extended help enabled)
Copyright (C) 2000-2013 The PARI Group
PARI/GP is free software, covered by the GNU General Public License, and comes WITHOUT ANY WARRANTY WHATSOEVER.
Type ? for help, \q to quit.
Type ?12 for how to get moral (and possibly technical) support.
parisize = 4000000, primelimit = 500000
(10:53) gp > ((2+I)^8-1)/3
%1 = -176 - 112*I
(10:54) gp > ((2+I)^48-1)/7
%2 = -8220080432083104 - 2221404619138848*I
(10:55) gp > ((2+I)^120-1)/11
%3 = 48335053046044394818188476307133621695792 - 62299385456398106436997673432684416797456*I
(10:55) gp >\begin{flushright}
\end{flushright}

[p] **conjecture pertaining to Gaussian integers** by akdevaraj Apr 24Let the base be a Gaussian integer = a + ib. Let p be a prime
number of shape 4m + 3. Then ((a + ib)^(p^2-1) - 1) == 0 (mod p).
This is subject to the base, a + ib and p being co-prime,

[p] **conjecture pertaining to Gaussian integers** by akdevaraj Apr 24Let the base be a Gaussian integer = a + ib. Let p be a prime
number of shape 4m + 3. Then ((a + ib)^(p^2-1) - 1) == 0 (mod p).
This is subject to the base, a + ib and p being co-prime,