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PlanetMath is a virtual community which aims to help make mathematical knowledge more accessible. PlanetMath's content is created collaboratively: the main feature is the mathematics encyclopedia with entries written and reviewed by members. The entries are contributed under the terms of the Creative Commons By/Share-Alike License in order to preserve the rights of authors, readers and other content creators in a sensible way. We use LaTeX, the lingua franca of the worldwide mathematical community.

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Latest Messages  

[P] Application of failure functions - indirect primality test by akdevaraj Jul 1
Consider integers of the form x^2 + 1. The relevant failure functions pertaining to f(x) = x^2 + 1 are x = 1 +2*k, 2 +5*k, 4 + 17k etc. All the values of x not covered by the above are such that f(x) are prime and these need not be tested for primality. Here k belongs to Z.

[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).