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6. Discussion

Type of Math Object: 
Feature
Major Section: 
Research
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Thanks for the references. Thomas Edison scaled down the building blocks of electricity to economically feasible units. Edison’s first scaled model was 1/3 copper, cost-wise. The scaling down of an economic system to finite units was first implemented by Middle Kingdom Egyptians, a finite unit fraction methodology that has not been fully decoded. Greeks used the finite model. Arabs and medieval scribes modified the multiplicationPlanetmathPlanetmath scaled model to a subtraction model, a system that ended with Galileo’s inversePlanetmathPlanetmathPlanetmathPlanetmath proportion square root method.

Numbers of the type 4m+1 are not prime in k(i). However their factors are prime. Example: 5 = (2+i)(2-i). If we take one of these as the base Fermat’s theorem works with respect to other co-primes of the type 4m+1. Examples: a) ((2-i)^12-1)/13 = 904 - 792i b)((2+i)^16-1)/17 = 9696 + 20832i

In one of my recent messages I had stated that there are four unities in k(i) viz 1, -1, i and -i. Fermat’s theorem holds true in k(i) when we keep this in mind. For example (2+I) and 3 are co-prime. Hence ((2+I)^4 + 1)/3 = -2 + 8i. I will be giving a few more examples in the next message.

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