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Old 04-27-2006   #1
ANTHONY.R.BROWN
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Default (flt) Demonstration By,anthony.r.brown

FERMATS LAST THEOREM DEMONSTRATION! BY, ANTHONY.R.BROWN (1998 SOLVED )

THE INFINITE MATHEMATICAL PATTERN OF CUBE NUMBERS!

BELOW IS MY DEMONSTRATION OF FERMATS LAST THEOREM,IT IS BASED ON THE INFINITE MATHEMATICAL PATTERN OF THE FIRST (10) CUBE NUMBERS AS A GROUP! YOU WILL SEE THAT THE LAST OR SINGLE NUMBER,FROM EACH OF THE (10) CUBE NUMBERS REPEATS ITSELF AT THE END OF EACH CUBE NUMBER, IN THE COLUMN,GIVEN IN BRACKETS () THIS PATTERN REPEATS ITSELF NO MATTER HOW LARGE OR SMALL THE CUBE NUMBERS ARE.
THE DEMONSTRATION IS! THAT BECAUSE YOU CANNOT ADD ANY TWO CUBE NUMBERS TOGETHER,TO MAKE A THIRD CUBE NUMBER,WITHIN ONE OF THE GROUPS, OR THE SAME WITHIN ANY TWO GROUPS,NO MATTER WHAT SIZE THE CUBE NUMBERS ARE! THEN YOU WILL NEVER BE ABLE TO MAKE A THIRD CUBE NUMBER,FROM ANY TWO CUBE NUMBERS.


Andrew wiles proof? (not possible! 100 %) of ( FLT ) is far too long! And contains math not really needed,with such a simple problem such as ( FLT ) plus only a few people in the world can really understand it.

Fermat stated the words below!

I HAVE DISCOVERED A TRULY MARVELLOUS DEMONSTRATION [ OF THIS GENERAL THEOREM ] WHICH THIS MARGIN IS TOO NARROW TO CONTAIN.

I believe my Demonstration must have been along the same lines as Fermats if not the same.
To understand ( FLT ) the answer is right there at the beginning, just like time itself, everything you need to know is in the first ten cube numbers!
The fact that all the numbers are used from 0 to 9 at the end of the cube numbers,the fact that some of the cubes are odd,the fact that some of the cubes are even,the fact that the cubes as a group look random!
The first ten cubes can be checked amongst themselves, for any two cubes that may make a third,and checked with any other ten as part of their group.
The infinite unique pattern is what makes everything work! Once you understand how cubes are made,then you have found all the cubes!
p.'s except the last!! The last case is unsolvable! for this reason its impossible to have a 100 % Proof! ( and applies to any infinite math problem ) only a Demonstration,as Fermat himself said!




BELOW THE FIRST TEN CUBE NUMBERS.

CUBE = (1): PATTERN = (1): COUNT = 1
CUBE = (8): PATTERN = (8): COUNT = 2
CUBE = 2(7): PATTERN = 2(7): COUNT = 3
CUBE = 6(4): PATTERN = 6(4): COUNT = 4
CUBE = 12(5): PATTERN = 12(5): COUNT = 5
CUBE = 21(6): PATTERN = 21(6): COUNT = 6
CUBE = 34(3): PATTERN = 34(3): COUNT = 7
CUBE = 51(2): PATTERN = 51(2): COUNT = 8
CUBE = 72(9): PATTERN = 72(9): COUNT = 9
CUBE = 100(0): PATTERN = (0): COUNT = 10

BELOW THE NEXT TEN.

CUBE = 133(1): PATTERN = (1): COUNT = 11
CUBE = 172(8): PATTERN = (8): COUNT = 12
CUBE = 219(7): PATTERN = 2(7): COUNT = 13
CUBE = 274(4): PATTERN = 6(4): COUNT = 14
CUBE = 337(5): PATTERN = 12(5): COUNT = 15
CUBE = 409(6): PATTERN = 21(6): COUNT = 16
CUBE = 491(3): PATTERN = 34(3): COUNT = 17
CUBE = 583(2): PATTERN = 51(2): COUNT = 18
CUBE = 685(9): PATTERN = 72(9): COUNT = 19
CUBE = 800(0): PATTERN = (0): COUNT = 20

AND THE NEXT TEN ETC.!

CUBE = 926(1): PATTERN = (1): COUNT = 21
CUBE = 1064(8): PATTERN = (8): COUNT = 22
CUBE = 1216(7): PATTERN = 2(7): COUNT = 23
CUBE = 1382(4): PATTERN = 6(4): COUNT = 24
CUBE = 1562(5): PATTERN = 12(5): COUNT = 25
CUBE = 1757(6): PATTERN = 21(6): COUNT = 26
CUBE = 1968(3): PATTERN = 34(3): COUNT = 27
CUBE = 2195(2): PATTERN = 51(2): COUNT = 28
CUBE = 2438(9): PATTERN = 72(9): COUNT = 29
CUBE = 2700(0): PATTERN = (0): COUNT = 30



EXAMPLE BELOW : TRY TO FIND IF THE TWO NUMBERS BELOW ADD TOGETHER MAKE A CUBE NUMBER!

2685619 + 4173281 = 6858900

Following what I have said in my Demonstration,all cube numbers are made in the same way,the infinite pattern is unique in the fact that the numbers 0 to 9 are only used once as in PATTERN A, at the end of the cubes numbers,within each group of any ten! plus more proof further on.
What it is like is a Mathematical engine that produces the cube numbers in unique groups of ten,starting from the first group of ten onwards Infinitely.
The sum of the two numbers above ( 6858900 ) is not a cube number! the reason its not a cube number is because it does not fit in any of the groups of ten,that are produced!
The nearest cube number too ( 6858900 ) is ( 6859000 ) this cube number is part of the 19 th Group given below,and is just before the start of the 20 th Group.
I will explain more how the Demonstration works below!


19 th Group

CUBE = 5929741 : PATTERN A = (1)
CUBE = 6028568 : PATTERN A = (8)
CUBE = 6128487 : PATTERN A = 2(7)
CUBE = 6229504 : PATTERN A = 6(4)
CUBE = 6331625 : PATTERN A = 12(5)
CUBE = 6434856 : PATTERN A = 21(6)
CUBE = 6539203 : PATTERN A = 34(3)
CUBE = 6644672 : PATTERN A = 51(2)
CUBE = 6751269 : PATTERN A = 72(9)
CUBE = 6859000 : PATTERN A = (0)

20 th Group

CUBE = 6967871 : PATTERN A = (1)
CUBE = 7077888 : PATTERN A = (8)
CUBE = 7189057 : PATTERN A = 2(7)
CUBE = 7301384 : PATTERN A = 6(4)
CUBE = 7414875 : PATTERN A = 12(5)
CUBE = 7529536 : PATTERN A = 21(6)
CUBE = 7645373 : PATTERN A = 34(3)
CUBE = 7762392 : PATTERN A = 51(2)
CUBE = 7880599 : PATTERN A = 72(9)
CUBE = 8000000 : PATTERN A = (0)


MORE INFORMATION BELOW ON HOW MY DEMONSTRATION WORKS!

The next pattern is the group of numbers that are produced, by taking away the cube numbers starting with the largest and working backwards,as in the first group below,so 1000 - 729 = (271),729 - 512 = (217),512 - 343 = (169),343 - 216 = (127),216 -125 = (91),125 - 64 = (61),64 - 27 = (37),27 - 8 = (19),8 - 1 = (7).
What we now have is the second unique pattern (B),that shows us we have a group of related cube numbers,the end numbers are made up of 7,9,7,1,1,7,9,7,1 in brackets ()

1 st Group PATTERN B

CUBE = 1
DIFFERENCE = 7 : PATTERN B = (7)
CUBE = 8
DIFFERENCE = 19 : PATTERN B = (9)
CUBE = 27
DIFFERENCE = 37 : PATTERN B = (7)
CUBE = 64
DIFFERENCE = 61 : PATTERN B = (1)
CUBE = 125
DIFFERENCE = 91 : PATTERN B = (1)
CUBE = 216
DIFFERENCE = 127 : PATTERN B = (7)
CUBE = 343
DIFFERENCE = 169 : PATTERN B = (9)
CUBE = 512
DIFFERENCE = 217 : PATTERN B = (7)
CUBE = 729
DIFFERENCE = 271 : PATTERN B = (1)
CUBE = 1000

Now we move on to pattern (C) this pattern is made by dividing the actual COUNT position,in relation to where the cube numbers are from the start onwards! NOTE: the resulting numbers are always WHOLE numbers! the end numbers are made up of 1,4,9,6,5,6,9,4,1,0 in brackets ()


1 st Group PATTERN C

CUBE = 1 : COUNT = 1 : EQUALS 1 : PATTERN C = (1)
CUBE = 8 : COUNT = 2 : EQUALS 4 : PATTERN C = (4)
CUBE = 27 : COUNT = 3 : EQUALS 9 : PATTERN C = (9)
CUBE = 64 : COUNT = 4 : EQUALS 16 : PATTERN C = (6)
CUBE = 125 : COUNT = 5 : EQUALS 25 : PATTERN C = (5)
CUBE = 216 : COUNT = 6 : EQUALS 36 : PATTERN C = (6)
CUBE = 343 : COUNT = 7 : EQUALS 49 : PATTERN C = (9)
CUBE = 512 : COUNT = 8 : EQUALS 64 : PATTERN C = (4)
CUBE = 729 : COUNT = 9 : EQUALS 81 : PATTERN C = (1)
CUBE = 1000 : COUNT = 10 : EQUALS 100 : PATTERN C = (0)




Now lets see if the number ( 6858900 ) the sum of the two numbers is a cube number or not! I will put the number in the group where the number is closest matched,which happens to be the tenth place within the 19 th Group below,and replace the true cube number ( 6859000 ) with the number ( 6858900 ) and see what happens to the patterns A,B,C!


19 th Group

CUBE = 5929741 : PATTERN A = (1) : COUNT = 181 : EQUALS 32761 : PATTERN C = (1)
DIFFERENCE = 98827 : PATTERN B = (7)
CUBE = 6028568 : PATTERN A = (8) : COUNT = 182 : EQUALS 33124 : PATTERN C = (4)
DIFFERENCE = 99919 : PATTERN B = (9)
CUBE = 6128487 : PATTERN A = 2(7) : COUNT = 183 : EQUALS 33489 : PATTERN C = (9)
DIFFERENCE = 101017 : PATTERN B = (7)
CUBE = 6229504 : PATTERN A = 6(4) : COUNT = 184 : EQUALS 33856 : PATTERN C = (6)
DIFFERENCE = 102121 : PATTERN B = (1)
CUBE = 6331625 : PATTERN A = 12(5) : COUNT = 185 : EQUALS 34225 : PATTERN C = (5)
DIFFERENCE = 103231 : PATTERN B = (1)
CUBE = 6434856 : PATTERN A = 21(6) : COUNT = 186 : EQUALS 34596 : PATTERN C = (6)
DIFFERENCE = 104347 : PATTERN B = (7)
CUBE = 6539203 : PATTERN A = 34(3) : COUNT = 187 : EQUALS 34969 : PATTERN C = (9)
DIFFERENCE = 105469 : PATTERN B = (9)
CUBE = 6644672 : PATTERN A = 51(2) : COUNT = 188 : EQUALS 35344 : PATTERN C = (4)
DIFFERENCE = 106597 : PATTERN B = (7)
CUBE = 6751269 : PATTERN A = 72(9) : COUNT = 189 : EQUALS 35721 : PATTERN C = (1)

Below is the tenth place!

Below is the true cube number,and shows all three Patterns working as normal!

DIFFERENCE = 107731 : PATTERN B = (1)
CUBE = 6859000 : PATTERN A = (0) : COUNT = 190 : EQUALS 36100 : PATTERN C = (0)

Below is the new number,you will notice the number works with only two of the patterns,but is way out with the third,i.e. not a WHOLE number! and ending with the wrong number in the () this proves its not a cube number!

DIFFERENCE = 107631 : PATTERN B = (1)
CUBE = 6858900 : PATTERN A = (0) : COUNT = 190 : EQUALS 36099.473 : PATTERN C = (int(9)? or (3)? both are wrong!



MORE INFORMATION BELOW ON HOW MY DEMONSTRATION WORKS!

As I have already said,all cube numbers are made the same way using what I would like to call a MATHEMATICAL ENGINE!
the process is from the first single cube number (1) onwards.
The most important numbers are the end numbers in brackets () the reason they are the most important is because they are the end of the process for making cube numbers! they are if you like the TRUTH numbers! its a bit like the numbers go round and round mathematically,and eventually make a whole cube number!
I have put forward three patterns A,B,C that show how these TRUTH numbers are present in any group of ten cube numbers,I am again giving the 1st and 19th Groups as examples!
The size of the cube numbers never changes how these TRUTH numbers are made! another way of looking at what im saying is that the cube numbers in the 1st Group are the same as in the 19th Group by the way they are made, and both are the same as any other group! size does not affect the TRUTH number results!
So if these two groups are the same,then trying to find if any two cube numbers make a third ,within the first group! is the same as trying with any other group,then after that test! we only need to test two groups against each other,because the maximum test is two from one group,or one from each group!
Now if we want to find out if a group of any ten numbers are cube numbers,the ten numbers must pass the three tests,they must conform to the patterns A,B,C and at the same time if we want to test if any single number is a cube number,this can be done by finding if it fits in with the nine cube numbers that are related to it,as part of its own group!.




PATTERN (A) = 1,8,7,4,5,6,3,2,9,0 in brackets ()

PATTERN (B) = 7,9,7,1,1,7,9,7,1 in brackets ()

PATTERN (C) = 1,4,9,6,5,6,9,4,1,0 in brackets ()


1 st Group

CUBE = 1: PATTERN A = (1) : COUNT = 1 : EQUALS 1 : PATTERN C = (1)
DIFFERENCE = 7 : PATTERN B = (7)
CUBE = 8: PATTERN A = (8) : COUNT = 2 : EQUALS 4 : PATTERN C = (4)
DIFFERENCE = 19 : PATTERN B = (9)
CUBE = 27: PATTERN A = (7) : COUNT = 3 : EQUALS 9 : PATTERN C = (9)
DIFFERENCE = 37 : PATTERN B = (7)
CUBE = 64: PATTERN A = (4) : COUNT = 4 : EQUALS 16 : PATTERN C = (6)
DIFFERENCE = 61 : PATTERN B = (1)
CUBE = 125: PATTERN A = (5) : COUNT = 5 : EQUALS 25 : PATTERN C = (5)
DIFFERENCE = 91 : PATTERN B = (1)
CUBE = 216: PATTERN A = (6) : COUNT = 6 : EQUALS 36 : PATTERN C = (6)
DIFFERENCE = 127 : PATTERN B = (7)
CUBE = 343: PATTERN A = (3) : COUNT = 7 : EQUALS 49 : PATTERN C = (9)
DIFFERENCE = 169 : PATTERN B = (9)
CUBE = 512: PATTERN A = (2) : COUNT = 8 : EQUALS 64 : PATTERN C = (4)
DIFFERENCE = 217 : PATTERN B = (7)
CUBE = 729: PATTERN A = (9) : COUNT = 9 : EQUALS 81 : PATTERN C = (1)
DIFFERENCE = 271 : PATTERN B = (1)
CUBE = 1000: PATTERN A = (0) : COUNT = 10 : EQUALS 100 : PATTERN C = (0)




19 th Group

CUBE = 5929741 : PATTERN A = (1) : COUNT = 181 : EQUALS 32761 : PATTERN C = (1)
DIFFERENCE = 98827 : PATTERN B = (7)
CUBE = 6028568 : PATTERN A = (8) : COUNT = 182 : EQUALS 33124 : PATTERN C = (4)
DIFFERENCE = 99919 : PATTERN B = (9)
CUBE = 6128487 : PATTERN A = (7) : COUNT = 183 : EQUALS 33489 : PATTERN C = (9)
DIFFERENCE = 101017 : PATTERN B = (7)
CUBE = 6229504 : PATTERN A = (4) : COUNT = 184 : EQUALS 33856 : PATTERN C = (6)
DIFFERENCE = 102121 : PATTERN B = (1)
CUBE = 6331625 : PATTERN A = (5) : COUNT = 185 : EQUALS 34225 : PATTERN C = (5)
DIFFERENCE = 103231 : PATTERN B = (1)
CUBE = 6434856 : PATTERN A = (6) : COUNT = 186 : EQUALS 34596 : PATTERN C = (6)
DIFFERENCE = 104347 : PATTERN B = (7)
CUBE = 6539203 : PATTERN A = (3) : COUNT = 187 : EQUALS 34969 : PATTERN C = (9)
DIFFERENCE = 105469 : PATTERN B = (9)
CUBE = 6644672 : PATTERN A = (2) : COUNT = 188 : EQUALS 35344 : PATTERN C = (4)
DIFFERENCE = 106597 : PATTERN B = (7)
CUBE = 6751269 : PATTERN A = (9) : COUNT = 189 : EQUALS 35721 : PATTERN C = (1)
DIFFERENCE = 107731 : PATTERN B = (1)
CUBE = 6859000 : PATTERN A = (0) : COUNT = 190 : EQUALS 36100 : PATTERN C = (0)



THE ABOVE EXAMPLES CLEARLY SHOW ALL CUBE NUMBERS ARE MADE THE SAME WAY! SO THE METHODS USED TO SEE IF ANY TWO NUMBERS MAKE A CUBE NUMBER, WILL ALWAYS BE THE SAME! REGARDLESS OF THE SIZE OF THE NUMBERS.


Please forward any comments to me at my E-MAIL address below,or to any Forum this (FLT) Demonstration is on!

TONYSWWW@YAHOO.CO.UK

A.R.B
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Old 04-27-2006   #2
Mr. Hui


 
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A little background on Fermat's Last Theorem:

There are no non-zero integers x, y, and z such that xn + yn = zn where n is an integer greater than 2.

I'm always fascinated with number theory. I will need some time to study your work.
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