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Latest Messages  

[P] Some results pertaining to Z(i).(contd) by akdevaraj Jun 26
In the case of 3-factor composites Euler's generalisation of Fermat's theorem works in the ring of Gaussian integers irrespective of the shape of the prime factors.

[P] Some results pertaining to Z(i). by akdevaraj Jun 25
a) Fermat's theorem works only in the case of primes of shape 4m+1. b)Euler's generalisation of Fermat's theorem works only when composite numbers each of which is prime of shape 4m + 1 ( in the case of two-member composites -the only exception being 15 ). (to be continued ).

[P] Euler's generalisation of Fermat's theorem ....... by akdevaraj Jun 23
This theorem states that if a^x + c = m then a^(x+k*phi(m)) +c is congruent to 0 (mod m). Here a,x and c belong to N, x is not fixed. k also belongs to N. Ref: ISSN 1550 - 3747

[P] Search engine by akdevaraj Jun 22
Search engine is still not functioning.

[P] Messages by akdevaraj Jun 22
I am not able to post messages; Unlord should do something about this.

[P] Euler's generalisation of Fermat's theorem ....... by akdevaraj Jun 21
Euler's generalisation of Fermat's theorem - a further generalisation -- this is the title of a paper presented at the Hawaii Internation Conference in 2004. This theorem works in the ring of Gaussian integers also. Ref: ISSN # 1550-3747

[P] Euler's generalisation of Fermat's theorem ....... by akdevaraj Jun 20
Ref: ISSN # 1550 - 3747 If any member is interested I can give further details.

[P] Euler's generalisation of Fermat's theorem .......(contd) by akdevaraj Jun 19
Ref: ISSN # 1550- 3747. In Z the theorem states that if a^n + c = m then a^(n +k* phi(m) +c is congruent to 0 mod(m). Here n and k belong to N. In Z(i) this is also true, phi(m) being only Eulerphi of the real part of m.

[P] Euler's generalisation of Fermat's theorem ....... by akdevaraj Jun 18
I had submitted a paper at the Hawaii International conference on mathematics entitled " Euler's generalisation of Fermat's theorem - a further generalisation in 2004 ". That paper pertained to the ring of integers. I now find that it is true in the ring of Gaussian integers too.

[P] Euler's generalisation of Fermat's theorem - a further gene by akdevaraj Jun 16
"Euler's generalisation of Fermat's theorem - a further generalisation" is the title of a paper presented at Hawaii International conference on Mathematics in 2004. The theorem is true in the ring of Gaussian integers too. Ref: ISSN # 1550 - 3747

[P] Euler's generalisation of Fermat's theorem - a further gen by akdevaraj Jun 16
Ref: ISSN # 1550 - 3747

Measure things by SKungen Jun 13
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[P] Carmichael numbers by akdevaraj Jun 12
There are no Carmichael numbers in Z(i). 561, which is the smallest Carmichael number in Z, is only a pseudoprime in Z(i).(one of the valid bases is (10 +i). Similarly 1105 is only a pseudoprime in Z(i)- one of the bases is (6 + i).

[P] Deep looking at formulas in by ayjara Jun 11
Deep looking at formulas in pdf figure, I reach this: %%% begin Matlab code %%% a3 = a a2 = b a1 = c a0 = c T1 = -a3/4; T2 = a2^2 - 3*a3*a1 + 12*a0; T3 = (2*a2^3 - 9*a3*a2*a1 + 27*a1^2 + 27*a3^2*a0 - 72*a2*a0)/2; T4 = (-a3^3 + 4*a3*a2 - 8*a1)/32; T5 = (3*a3^2 - 8*a2)/48; R1 = power(T3^2 - T2^3, 1/2); % power -> 1st primitive root R2 = power(T3 + R1, 1/3); R3 = (1/12)*(T2/R2 + R2); R4 = power(T5 + R3, 1/2); R5 = 2*T5 - R3; if abs(T4) < 1e-10 && abs(R4) < 1e-10 % ideally: if T4 = R4 = 0 R6 = 1; R4 = 0; else R6 = T4/R4; end z(1,1) = T1 + R4 + power(R5 + R6, 1/2); z(2,1) = T1 + R4 - power(R5 + R6, 1/2); z(3,1) = T1 - R4 + power(R5 - R6, 1/2); z(4,1) = T1 - R4 - power(R5 - R6, 1/2); %%% end Matlab code %%% This code works in most of cases I have tested. But, not in "potato_jack" example.