## New Articles

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*Ref*]**Sophomore's dream**by pahioJul 9[

*Res*]**examples of growth of perturbations in chemical or...**by rspuzioMay 24[

*Ref*]**proof of Stirling's approximation**by rspuzioMay 8[

*Res*]**Example of stochastic matrix of mapping**by rspuzioApr 23[

*Res*]**6. Discussion**by rspuzioApr 20[

*Res*]**5. Entanglement**by rspuzioApr 20[

*Res*]**4. Measurement**by rspuzioApr 20[

*Res*]**3. Distributed dynamical systems**by rspuzioApr 20[

*Res*]**2. Stochastic maps**by rspuzioApr 20[

*Res*]**1. Introduction**by rspuzioApr 19[

*Ref*]**Oseledets multiplicative ergodic theorem**by FilipeMar 18[

*Ref*]**Furstenberg-Kesten theorem**by FilipeMar 18[

*Ref*]**multiplicative cocycle**by FilipeMar 18[

*Ref*]**remainder term series**by pahioMar 17## Latest Messages

Jul 21

Jul 20

Jul 19

Jul 17

Jul 14

Jul 11

Jun 30

Jun 25

Jun 23

Jun 23

Jun 20

Jun 16

Jun 16

Jun 15

This base, however , does not work in the case of primes having
shape 4m+3. A base that works is 1 + i. Example ((1+i)^102 + I)/103
= -21862134113449i.

Jul 20

What is the nature of a, the base? When p has the shape 4m+1
a has the shape of a prime factor of a number having the same shape.
Example: Let p = 61. Then ((4 + i)^60 - 1 )/61 =
-71525089284120116591639000327021600 + 11369162311133702688684197835211600i

Jul 19

Before giving some further generalisations let me give some examples: case a)
((1+I)^30 + I)/31 = -1057i. ((1 + i )^102 + i)/103 = -21862134113449i
Case b) ((1 + i)^12 - 1)/13 = -5. (( 1 + i ) ^100 - 1)/101 = -11147523830125

Jul 17

Although Hardy and Wright have formulated the above theorem in their book ("An introduction
to he theory of numbers " we can see how it works with the aid of software like pari.
The four examples illustrate this. Now for a few genralisations: a) If p is a prime
of form 4m+3, then ((a^(p-1)+ I)/p is congruent to 0 (mod(p)). b) If p is a prime
of form 4m+1, then ((a^(p-1) - 1)/p is congruent to 0 (mod(p)).

Jul 14

There are four unities in k(i) viz 1, -1, i and -i. Four examples are given
here to illustrate Fermat's theorem in k(i). a)((2+3i)^2-1)/3 = -2 +4i b)
((3+2i)^2 + 1)/3 = 2 + 4i c) ((10 + i)^2 + i)/3 = 33 + 7i and d) ((14 +i)^2 - i)/3 =
65 + 9i.

Jul 11

Considering 2 simplex tableau encountered when solving a linear program
http://i62.tinypic.com/9r80ic.jpg
determine the value of each of the following items(unknowns) : p q r that appear in tables
http://i61.tinypic.com/mcwx9u.jpg
And please if someone has another example like this one please give it to me>

Jun 30

I just read your article and it was totally great, it contains a lot of useful ideas, it is also written in organize manner,thanks for sharing this kind of article.
<a href="http://increasemyplays.com/buy-soundcloud-likes/">

Jun 25

Please see "sophomore's dream" in Wikipedia.

Jun 23

1.- Is False
2.- Is True
1.- Is False
1.- Is true, iff b is rational.
Regards,
Ronald.

Jun 23

Let our definition of a failure be a composite number which is also a multiple of 11.
Let the parent function be 2^n + 7 (n belongs to N ). Then n = 2 + Eulerphi(11) is
a failure function. Also n = 2^(1 + Eulerphi(Eulerphi(11)) is also a failure function.

Jun 20

Let our definition of a failure be a non-primitive polynomial in
x (x belongs to Z ). Let the parent function be the primitive
polynomial x^2 + x + 1. Then x generated by any of the
failure functions 1 + 3k, 2 + 7k etc when substituted in
the parent function yield failures i.e. non primitive polynomials.

Jun 16

This refers to " Non-linear failure functions and Automorphism.
The second-last line should read: When the relevant quotient is divided
by 17 we get a remainder = 5, a member of Z_17.

Jun 16

Let our definition of a failure be a composite number. Let the mother function
be the quadratic x^2 + 1 ( x belongs to Z ). When x =4, f(x) =17.
x = 4 + 17*k is a failure function. This is linear. The non -linear
failure function x = 38 + 17^(k+2) generates values of x, which
when substituted in f(x) we get multiples of 289. The relevant
quotients when divided by 17 yield the remainder 3, a member of Z_17.
Here k belongs to W.

Jun 15

Failure functions can be applied in the following areas:
a) Solving Diaphontine equations ( for copy of paper send
request to dkandadai@gmail.com
b) Indirect primality testing
c) In proving conjectures (see sketch proof )

## Latest Messages

Jul 21

Jul 20

Jul 19

Jul 17

Jul 14

Jul 11

Jun 30

Jun 25

Jun 23

Jun 23

Jun 20

Jun 16

Jun 16

Jun 15

This base, however , does not work in the case of primes having
shape 4m+3. A base that works is 1 + i. Example ((1+i)^102 + I)/103
= -21862134113449i.

Jul 20

What is the nature of a, the base? When p has the shape 4m+1
a has the shape of a prime factor of a number having the same shape.
Example: Let p = 61. Then ((4 + i)^60 - 1 )/61 =
-71525089284120116591639000327021600 + 11369162311133702688684197835211600i

Jul 19

Before giving some further generalisations let me give some examples: case a)
((1+I)^30 + I)/31 = -1057i. ((1 + i )^102 + i)/103 = -21862134113449i
Case b) ((1 + i)^12 - 1)/13 = -5. (( 1 + i ) ^100 - 1)/101 = -11147523830125

Jul 17

Although Hardy and Wright have formulated the above theorem in their book ("An introduction
to he theory of numbers " we can see how it works with the aid of software like pari.
The four examples illustrate this. Now for a few genralisations: a) If p is a prime
of form 4m+3, then ((a^(p-1)+ I)/p is congruent to 0 (mod(p)). b) If p is a prime
of form 4m+1, then ((a^(p-1) - 1)/p is congruent to 0 (mod(p)).

Jul 14

There are four unities in k(i) viz 1, -1, i and -i. Four examples are given
here to illustrate Fermat's theorem in k(i). a)((2+3i)^2-1)/3 = -2 +4i b)
((3+2i)^2 + 1)/3 = 2 + 4i c) ((10 + i)^2 + i)/3 = 33 + 7i and d) ((14 +i)^2 - i)/3 =
65 + 9i.

Jul 11

Considering 2 simplex tableau encountered when solving a linear program
http://i62.tinypic.com/9r80ic.jpg
determine the value of each of the following items(unknowns) : p q r that appear in tables
http://i61.tinypic.com/mcwx9u.jpg
And please if someone has another example like this one please give it to me>

Jun 30

I just read your article and it was totally great, it contains a lot of useful ideas, it is also written in organize manner,thanks for sharing this kind of article.
<a href="http://increasemyplays.com/buy-soundcloud-likes/">

Jun 25

Please see "sophomore's dream" in Wikipedia.

Jun 23

1.- Is False
2.- Is True
1.- Is False
1.- Is true, iff b is rational.
Regards,
Ronald.

Jun 23

Let our definition of a failure be a composite number which is also a multiple of 11.
Let the parent function be 2^n + 7 (n belongs to N ). Then n = 2 + Eulerphi(11) is
a failure function. Also n = 2^(1 + Eulerphi(Eulerphi(11)) is also a failure function.

Jun 20

Let our definition of a failure be a non-primitive polynomial in
x (x belongs to Z ). Let the parent function be the primitive
polynomial x^2 + x + 1. Then x generated by any of the
failure functions 1 + 3k, 2 + 7k etc when substituted in
the parent function yield failures i.e. non primitive polynomials.

Jun 16

This refers to " Non-linear failure functions and Automorphism.
The second-last line should read: When the relevant quotient is divided
by 17 we get a remainder = 5, a member of Z_17.

Jun 16

Let our definition of a failure be a composite number. Let the mother function
be the quadratic x^2 + 1 ( x belongs to Z ). When x =4, f(x) =17.
x = 4 + 17*k is a failure function. This is linear. The non -linear
failure function x = 38 + 17^(k+2) generates values of x, which
when substituted in f(x) we get multiples of 289. The relevant
quotients when divided by 17 yield the remainder 3, a member of Z_17.
Here k belongs to W.

Jun 15

Failure functions can be applied in the following areas:
a) Solving Diaphontine equations ( for copy of paper send
request to dkandadai@gmail.com
b) Indirect primality testing
c) In proving conjectures (see sketch proof )