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Latest Messages  

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

[p] Fermat's theorem works when the base is a Gaussian integer by akdevaraj 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?

[p] On Measurement Assessment and Division Matrices by ProfHasan Apr 9
http://jsaer.com/download/vol-3-iss-6-2016/JSAER2016-03-06-233-237.pdf

[p] Division of Matrices by ProfHasan Apr 9
http://jsaer.com/download/vol-3-iss-5-2016/JSAER2016-03-05-101-104.pdf

[p] Division of Matrices by ProfHasan Apr 9
http://jsaer.com/download/vol-3-iss-5-2016/JSAER2016-03-05-101-104.pdf

[p] Division of Matrices by ProfHasan Apr 9
http://jsaer.com/download/vol-3-iss-5-2016/JSAER2016-03-05-101-104.pdf

[p] Division of Matrices by ProfHasan Apr 9
http://jsaer.com/download/vol-3-iss-5-2016/JSAER2016-03-05-101-104.pdf

[p] Division of Matrices by ProfHasan Apr 9
In this study, we deal with functions from the square matrices to square matrices, which the same order. Such a function will be called a linear transformation, defined as follows: Let Mn(R) be a set of square matrices of order n, n ϵ S, and A be regular matrix in Mn(R), then the special function TA: Mn(R) → Mn(R) X T X A   X A   is called a linear transformation of Mn(R) to Mn(R) the following two properties are true for all X,Y ϵ Mn(R), and scalars α ϵ R: i. TA (X+Y) = TA(X) + TA(Y). (We say that TA preserves additivity) ii. TA(αX)= αTA(X) (We say that TA preserves scalar multiplication) In this case the matrix A is called the standard matrix of the function TA. Here, we transfer some well known properties of linear transformations to the above defined elements in the set all { TA: A regular in Mn(R)} [1]

[P] isolated square free numbers by akdevaraj Feb 27
I 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 27
I 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 20
So that, the first twin isolated square-free numbers are $ {17,19}$, sorry.

[p] Euler's generalisation of Fermat's theorem ....... by akdevaraj Feb 17
This 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 17
This 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 27
Fermat'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