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My Thesis on Divisibility (opposite series theory) - GOD Rule

  • #1
  • Quote
  • First Post: Edited 8:00pm Sep 24, 2025 7:32pm | Edited 8:00pm
basics:


Easy numbers: (there are 4 easy numbers)
easy number is the number when you reciprocate it () the result will be only on digit after decimal point. Therefore it is an indication to know immediatly divisibilty of any big numbers by that number
1/1=1.0 ,,,,,, 1/2 = 0.5 ,,,,,, 1/5 =0.2 ,,,,,,,, 1/10=0.1
the final result is only 1 digit after decimal point . . therefore the are "easy number" to decide thier multiples

NUMBER 1: any number is divisble by 1

NUMBER 2: if the last digit of the number is even then the whole number is divisble by 2

now to my big theory on division .. it is a historic invention . . .


NUMBER 5: if the last digit of the number is 0 or 5 then the whole number is divisble by 5

NUMBER 10: if the last digit of the number is 0 then the whole number is divisble by 10
..
, , , ,
rule: always you need 2 digits number, we name it secret or cypher number, so that when applied to another number in some addtion/subtravtion way, the final result will be the same number or one of its mutiples . . .

let us start with NUMBER4 . . we need to know the ecact rule to determine if any number is divisble by 4 or not. . .
my BIG THEORY has the solution . .
i
since 4 is only one digit, we need the any 2 digits number that is divisble by 4,
the nearest one is 12 ... . 3*4=12

when you take the reciprocal of 4 (e.u 1/4) the answer is 0.25
0.25: two digits after decimal
therefore among my new discoveries, you need only the last two digits of any number to decide if that number is divisble by 4 or not.
12 is the nearest 4 multiple, and you need only 2 exponents of this number elements, one positive and another os negative

12 : elements: 1 and -2 (or -1 and +2)

1 from down to up
-2 from up to down
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after picture process
number 4 secrer numbers are -2 and +1

example: is 632 is divisble by 4?

you need according to my theory 1, only the last 2 digits (32) .. thery are enough to decide:
3(-2)+2*(+1) = -6+2 = 4 .. result is 4 which is 4-multiples, therefore 632 is divisble by 4 . .
the first reader of this post is the first one in the history knows this 4 secret ,, easy rule . . .
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  • #2
  • Quote
  • Edited 8:37pm Sep 24, 2025 8:27pm | Edited 8:37pm
NUMBER 3
proof of the famous rule: if you sum up all number digits, if the result is divisble by 3, then the whole number is divisble by 3
look at the final results of exponents dot product . . all end with +1
that mean: multiple each digit by 1, the add all . .
but my theory exposed anonther ways
for 2 digits number , for example 42 . . you can use series +1 +1 or you can use also -2 +1
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42: 4*(+1)+2*(+1) = 4+2 = 6 which is divisble by 3, then 42 is divisble by 3
also you can use series -2 +1

4*(-2) + 2*(+1) = -8 + 2 = -6 which is divisble by 3, then 42 is divisble by 3
or you can use +2 -1, ,,,,,, 42: 4*2 - 1*2 = 8-4=6

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on picture i use my second theory and my thrid theory
Second theory(useless-content elimination): eliminite 3-contents of any number is greater than or equal 3
therfore i change +4 to +1 , since +4 = +3+1 ,,,, yes +4 = +1

Third theory(complement theory): you had better lower the numbers to the mots possible degree

for eample -2 it complement to 3 is +1
using +1 is easier than using -2

look at -8: first we eliminate 3-content which is -6 (-8 = -6 -2)
-8 = -2 ----> then we take comlement of -2 which is +1
complement is the number that will pass through 0 point on the numbers line to make a distance of 3

then for -2, +1 - (-2) = +3

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  • #3
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  • Sep 24, 2025 8:43pm Sep 24, 2025 8:43pm
NUMBER 3
do not forget the rule of reciporcal and its impact on your mind

1/3 = 0.33333333333333333333333333333333333333333333......

only one digit, like 1 , 2 ,5 ,10, but repeated for no-end (enfinity)
therefore: first expoenent is adequetd (since it is only one digit) , but applied for all number digits
in 4 case: you just take first two digits
in 3 case: ypu tale all number digits

we explain the scientigic reason here, and for the first time in history

3 rule: +1 +1 +1 +1 . . . . .

my theory also discovered anonther ways like +1 -2 +1 -2 +1 -2 . . . . which is the same as +1 +1 +1 , since +1 and -2 are complements . .


also ypu can use big numbers on last picture: +1 -2 +4 -8 +16 -32 . . .
it is a correct series, but is not practical !!! you are not stupid!!

Quiz:
what is the complement of +13 to 25 ?
ans: 13 - x = 25 ===== > x=-12
look: 13 to the right of 0 point on numbers-line, while -12 left to the 0-point
+12 is not the answer . .
25 here is a distance . . not a specific value
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  • #4
  • Quote
  • Edited 9:10pm Sep 24, 2025 8:49pm | Edited 9:10pm
NUMBER 6

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please divide one by 6

1/6 = 0.16666666666666666666666666666666666
what you see?? what my new-rules say?
here we have 2 differnrt digits, 1 and 6
1 is only one time, while 6 is repeated for the no-end . .

then:
we expect one specific cypher digit for ones postion, and other number digits to be multiplied by another number ..

do not forget thier famous rule: if number is divisble by 3 and is even: then it is divisble by 6 . . but now i prove thier empirical rule!!
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look
+1 with a series of -2s
or you can say -1 with a series of +2s, since if 60 for example is divisble by 6, also -60 is divisble by 6 . .
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  • #5
  • Quote
  • Sep 24, 2025 9:15pm Sep 24, 2025 9:15pm
NUMBER 6
look at +1, we see it only one time as expected, while -2 is repeated for ever ..
series . . . . . -2 -2 -2 -2 -2 -2 +1
Quiz:
is 51,366 is divisble by 6 ?
5(-2)+1(-2)+3(-2)+6(-2)+6(+1) = -10-2-6-12+6 = -30+6=-24
-24 is divisble by 6 then 51366 is divisble by 6

had better to sum since there is a common factor -2
(-2)(+5+1+3+6)+(+1)(+6) = (-2)(+15)+6=-30+6=-24 ===> +24
check using your calculator:
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thank you for Al-Otaibi Big Theory on Division . . .
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  • #6
  • Quote
  • Edited 9:31pm Sep 24, 2025 9:21pm | Edited 9:31pm
NUMBER 7

divide 1 by 7 ? what you see?
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is there any repition?
ans Yes
1/7 = 0 . 142857 142857 142857 142857 142857 ...... ...... . . . .

therefore what you expect now?
a series of 6 different cypher digits to determine if the number is divisble by 7 or not
later through my magic complement theory, we could reduce it to only three digits (three repeated elements)
repeated?
YES
since 1/7 fraction is repeated for ever . . .

look at 7 at the end of 142857 ?

ordinary people says it is 7, but Mohammed Al-Otaib says it is 6+1 . . .
that is the subtle diffrenece b/ me and other people . . and relaizition of this leads to my great dsicovey (DIVISIBILY BIG THEORY)

it is not my rule, it is the GOD rule, but iam the first one in the history who discovered , , ,

so? what is the secret of number 7 ?? what is its series ?

since the main part of 142857 142857 142857 is repeated each 6 digits, we need only first 6 exponents of the nearest 2 digits number that is divisble 7, it is 14 . . .
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  • #7
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  • Sep 24, 2025 9:59pm Sep 24, 2025 9:59pm
NUMBER 7
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then
7 series from left to right is:
-2 +4 -1 +2 -4 +1 -2 +4 -1 +2 -4 +1 . . . . . .
look six elements repeated for ever . ,
why 6 elements? refere to the last post?
why extended to no-end ??? refer to the last three posts . . .
elements are: +1 , -1 and +2 , -2 and +4 , -4

since 4 is avove 7/2, we has better use complements to make numbers lower in value:
+4 complement due to 7 is -3
-4 complement due to 7 is +3
therefore enhanced series is :

-2 +4 -1 +2 -4 +1 -2 +4 -1 +2 -4 +1 . . . . . .
to:
-2 -3 -1 +2 +3 +1 -2 -3 -1 +2 +3 +1 . . . . . .

look, eben sings are arranged better, three positives then three negatives and son on?

KIDS TEST: (to improve thier mental ability)
play with your kids and ask them if this number 8,638 is divisble by 7 or not ?

my fourth rule: you can start from any elemnt in the series . . just keep the sequence . . .
8638 is 4 digits, then pick up any 4-sequnce elements of the seris
you can use: -2-3-1+2
or you can use -3-1+2+3
or you can use -1+2+3 +1 , etc . .
or you can use uncomplemented series: +2 -4 +1 -2 or -4 +1 -2 +4 etc
you have 12 of choices . . .
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  • #8
  • Quote
  • Sep 24, 2025 10:01pm Sep 24, 2025 10:01pm
NUMBER 7
mathematics are collapsing!
example
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  • #9
  • Quote
  • Edited 10:25pm Sep 24, 2025 10:14pm | Edited 10:25pm
NUMBER 7

I prove it using 6 different sequencs , ,luxurious BIG DIVISION THEORY
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you can use also use +-+-+-+- .. method: +2 -4 +1 -2 +4 -1 . . . .
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more examples:
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  • #10
  • Quote
  • Edited 10:50pm Sep 24, 2025 10:31pm | Edited 10:50pm
NUMBER 8
we will follow the same steps:

first: divide 1 by 8 to check is it finite digit after decimal points or repeated digits . .
second: if repeated, who many digits are repeated
third: find the nearst two digits number that is divisble by 8 ... here it is 16
fourth: find opposite exponents till the number of finite or repeated digits
fifth: dot product of two expoenets series elements
sixth: remove the 8-content to simplify the process
seventh: you had better take complements of the previous step elemnt is greater than halve of 8

1/8=0.1250000000000000000000000
3 digits after decimal
therefore we need three exponents . . ^0, ^1 , ^2 for each cypher(16) element

and also, for big numbers like 87687288, just take the last three digits 288, it is enough to decide if teh number is 8-divisble or not
and ignore higher position digits , ,
thank you for AL-OTAIBI second rule
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therefore you have 4 options to decide on 8-divisbilty? ?
either:
+4 +2 +1
or
+4 -6 +1
or
-4 -2 -1
or
-4 +6 -1
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  • #11
  • Quote
  • Sep 24, 2025 11:03pm Sep 24, 2025 11:03pm
NUMBER 8

examples:
take only lowest three digits of the big number
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  • #12
  • Quote
  • Sep 25, 2025 12:02am Sep 25, 2025 12:02am
NUMBER 8
hence
also cypher 32 which is 8-divisble is suitble for oppsite exponents:
reason:
32
23
3*2-2*3=0

like 16
16
61
1*6-6*1=0

also 24 is a another choice . .
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look we end up to the same series elements . .
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  • #13
  • Quote
  • Edited 12:21am Sep 25, 2025 12:04am | Edited 12:21am
NUMBER 9


1/9=0.11111111111111111111111111111111 . .

wow, it seems to be very easy number comapred to six!!

so be 100% sure that the series will end to +1 +1 +1 +1 +1 .....

or
-1 -1 -1 -1 -1 -1 -1 -1 -1

let us apply it
1 digit repeated for no-end!! so apply the eries for all digits!! you need all number digits !

proof of thier famous rule:

since 0.111111..... is a repated for one digit, you need only two expoenents to check . .

result: +1 +1,
extend it for end
+1 +1 +1 +1 +1 . . ..
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therefore for any number just add its digits, if they sum up to 9-multiples, then the entire number is divisble by 9
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  • #14
  • Quote
  • Sep 25, 2025 12:29am Sep 25, 2025 12:29am
NUMBER 9
examples
repeated?
then start from any element from the series . .
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  • #15
  • Quote
  • Edited 12:52am Sep 25, 2025 12:32am | Edited 12:52am
NUMBER 9
and even if yoy choose 27 (9-multiples) instead of 18, you will reach to teh same result (same series)
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end to a series of one repeated elements -2 -2 -2 -2 -2 -2 . . .

pr +2 +2 +2 +2 +2 +2

therefore with number 9 any repeated series is qualified, but use the most simple one +1 +1 +1 +1

on picture also series +7 -2 +7 -2 +7 -2 . . . .are valid
+7 and -2 complements each other to 9 . . . . . . +7-(-2) =9
in prev pots if you remeber +8 -1 . .. are complements to 9 . . . . . . . +8-(-1) = 9

so you may think of +6 -3 +6 -3 +6 -3 . ..

and +5 -4 +5 -4 +5 -4 . . .

now you have many rules for NUMBER 9
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  • #16
  • Quote
  • Sep 25, 2025 12:58am Sep 25, 2025 12:58am
NUMBER 9
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is 771,219 divisble by 9 ??
let us use rule +5-4+5-4
+5 for even digits,,,,,, -r for odd digits ... due to series reciprocality"

7 7 1 2 1 9

5(7+1+1) - 4(7+2+9) = 5*9 - 4*18 = 45-72 = -27 (27 is 9 multiples)

or even:

4(7+1+1) -5(7+2+9) = 4*9 - 5*18 = 36-90= -54 (54 is 9-multiples)

look at the magic of math
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  • #17
  • Quote
  • Edited 3:17am Sep 25, 2025 12:59am | Edited 3:17am
NUMBER 11
the simplest number:
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therefore to check 11 divisibilty just add eben digits
and add odd digits
then subtract from each other . . .
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  • #18
  • Quote
  • Edited 3:21am Sep 25, 2025 1:02am | Edited 3:21am
NUMBER 11

example:
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  1. Twee
  2. |

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  • #19
  • Quote
  • Edited 3:50am Sep 25, 2025 3:24am | Edited 3:50am
NUMBER 12

12 itself is the lowest two digit number that is divisble by 12
we follow the same steps for 3, 4 and 6 .. they all share the lowest cypher number

also: you can check 4 condition and 3 condition .. if satisfied, then 12 condition is satisfied .. since 3*4=12
follow the asme steps:
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1/12 = 0.08333333333333333333333333333333

so there are 3 digits:
0 - one time
8 - one time
3 - repeated to no-end . .
in this case we expect a series of 3 elements . .
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look how it takes charatestics of both 3 and 4
12 series is . . . . . +4 +4 +4 +4 +4 +4 +4 +4 -2 +1

we know that -2 and +1 are common feature for 3 and 4 for the first two digits . .


for example 45 is 3-divisble: 3*15=45 ----> let us check: -2*4+1*5 = -8 +5 = -3 which is 3-divisble . .
this 3 rule for 2 digits number is among my new discoveries . . .


4: 76 ...... -2*7+1*6 = -14 + 6 = 8 ..... 4-divisble,,,, them 76 is 4-multiple . .

is 76 a 12-multiple ??
two digits mumber therefore take the last series two digits -2 and +1

76: -2*7+1*6 = 8 . . .. . not 12-divisble, then 76 is not a 12-multible
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  • #20
  • Quote
  • Sep 25, 2025 3:51am Sep 25, 2025 3:51am
is 115,590,972 divisble by 12 ??

115,590,972
4(1+1+5+5+9+0+9)-2*7+1*2 = 4*30-14+2 = 120-12 = 0 -12 = -12
ans: YES
WE REPLACE 120 BY 0, SINCE 120 is a 12-content
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NUMBER 13 secret discovery
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