how to determinate the unknowns of this simplex tableau

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# how to determinate the unknowns of this simplex tableau

Submitted by anouarattn on Fri, 07/11/2014 - 02:21

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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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## Versions

(v1) by anouarattn 2014-07-11

## Fermat's theorem in k(i)

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.

## Fermat's theorem in k(i) (c0ntd)

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)).

## Fermat's theorem in k(i) (c0ntd)

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

## Fermat's theorem in k(i) (c0ntd)

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## Fermat's theorem in k(i) (c0ntd)

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.