[P] **Application of failure functions - indirect primality test** by akdevaraj 10:46 amConsider 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 26In 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 25a) 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 23This 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 22Search engine is still not functioning.

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

[P] **Euler's generalisation of Fermat's theorem .......** by akdevaraj Jun 21Euler'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 20Ref: 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 19Ref: 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 18I 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 16Ref: ISSN # 1550 - 3747

**Measure things** by SKungen Jun 13>

[P] **Carmichael numbers** by akdevaraj Jun 12There 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).