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## Latest Messages

Apr 27
Happy to report that "Nick", on mersenneforum.org, has stated that my conjecture can be taken as proved.

Apr 27
Happy to report that "Nick", on mersenneforum.org, has stated that my conjecture can be taken as proved.

Apr 26
A 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}

Apr 24
Let 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,

Apr 24
Let 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,

Apr 24
Let 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,

Apr 24
Let 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,

Apr 24
Hi Jussi. Thanks will try.

Apr 24
Hi Jussi. Thanks will try.

Apr 20
Hi Deva, perhaps the entry 'theorem on sums of two squares by Fermat' may explain it or help this problem, Jussi

Apr 19
What puzzles me is that the theorem works when the base is a prime in the ring of Gaussian integers and the exponent is a prime of shape 4m + 1 but does not work when the exponent is a prime of shape 4m+3.Can any one throw some light on this?

Apr 9