[P] **isolated square free numbers** by akdevaraj Feb 27I prefer the definition as follows: prime numbers and composite
numbers in which each prime factor occurs only with exponent equal to
one. Examples of such composites: 6, 35, 65, 93....

[P] **isolated square free numbers** by akdevaraj Feb 27I prefer the definition as follows: prime numbers and composite
numbers in which each prime factor occurs only with exponent equal to
one. Examples of such composites: 6, 35, 65, 93....

[P] **I forgot the number 19.** by perucho Feb 20So that, the first twin isolated square-free numbers are $
{17,19}$, sorry.

[p] **Euler's generalisation of Fermat's theorem .......** by akdevaraj Feb 17This works even when the base is a Gaussian integer:
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
(17:50) gp > ((14+15*I)^104-1)/105
= -249662525598174865517621222098021785366399633335910441957688800663877876192221716937263714468906280908614454012799368615180549371243472 - 118511838209654103558982122027130965758920275429164915998560474682902951765213030198935065103035392002339412087987613469408163154998032*I
(17:51) gp >

[p] **Euler's generalisation of Fermat's theorem .......** by akdevaraj Feb 17This works even when the base is a Gaussian integer:
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
(17:50) gp > ((14+15*I)^104-1)/105
%1 = -249662525598174865517621222098021785366399633335910441957688800663877876192221716937263714468906280908614454012799368615180549371243472 - 118511838209654103558982122027130965758920275429164915998560474682902951765213030198935065103035392002339412087987613469408163154998032*I
(17:51) gp >

[p] **Fermat's theorem** by akdevaraj Jan 27Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1
and b) the exponent and base are co-prime.
((2+3*I)^16-1)/17
= -47977440 - 803040*I

[p] **Fermat's theorem** by akdevaraj Jan 27Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1
and b) the exponent and base are co-prime.
((2+3*I)^16-1)/17
%1 = -47977440 - 803040*I

[p] **Fermat's theorem** by akdevaraj Jan 27Fermat's theorem works even if the base is a Gausssian integer subject to a) the prime under consideration is of shape 4m+1
and b) the exponent and base are co-prime.
((2+3*I)^16-1)/17
%1 = -47977440 - 803040*I

[p] **An open invitation** by akdevaraj Jan 26Join maths corner on facebook. Procedure: join fb
and I can add you as member - your contributions are welcome.

[p] **Happy** by akdevaraj Jan 26Happy to see Pahio is again active on this site!

[p] **Happy** by akdevaraj Jan 26Happy to see Pahio is again active on this site!

[p] **Happy** by akdevaraj Jan 26Happy to see Pahio is again active on this site!

[p] **Happy** by akdevaraj Jan 26Happy to see Pahio is again active on this site!

[p] **1 11 111 1111…** by phongphanp Jan 51 11 111 1111...
This could be an example to here, the normal.