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[p] Fermat's theorem in k(i) (c0ntd) by akdevaraj Jul 21
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.

[p] Fermat's theorem in k(i) (c0ntd) by akdevaraj 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

[p] Fermat's theorem in k(i) (c0ntd) by akdevaraj 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

[p] Fermat's theorem in k(i) (c0ntd) by akdevaraj 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)).

[p] Fermat's theorem in k(i) by akdevaraj 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.

how to determinate the unknowns of this simplex tableau by anouarattn 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>

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[p] A good question by pahio Jun 25
Please see "sophomore's dream" in Wikipedia.

[p] easy exercice by Ron Castillo Jun 23
1.- Is False 2.- Is True 1.- Is False 1.- Is true, iff b is rational. Regards, Ronald.

[P] failure functions - another exampleL by akdevaraj 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.

[P] failure functions - another example by akdevaraj 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.

[P] A correction by akdevaraj 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.

[P] Non-linear failure functions and automorphism by akdevaraj 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.

[P] failure functions - applications by akdevaraj 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 )