Number, Number, and Numbers (un numéro, un numéro, et les numéros)
Every man has three dimensional features as a member of society, as a member of his family, and as a man facing the God.
So, Christ Jesus said to love the God as much as possible and love your neighbors as you love yourself.
Accordingly, we can recognize three factors in different directions, which is three-dimensional or cubic.
Therefore, the symbol of Christianity must be 3D.
SECTION I: X^13 = 63 mod 85
Here N, M, and X are integers;
X^3 = X x X x X, that is, the 3rd power of X.
Take up an equation: X^13 = 85 x N + 63
Then, what is X?
The answer is: X = surplus of (63^5) / 85 = 3, since 63^5 = 85 x M + 3.
Simply, X = 3.
Indeed, 3^13 = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3
= 1594323
= 85 x 18756 + 63
Incidentally, N = 18756 and M = 11675724.
Note that 85 = 17 x 5. And, the least common multiple of (17-1) and (5-1) is 16 which shares no common divisor with 13 but bigger than 13. For these numbers 13 and 16, 5 satisfies the equation: 13 x 5 = L x 16 + 1, with L an integer (L = 4). In this way, 5 in the above proof is obtained. --- (1)
In a practical use, a message sender encodes his message X to obtain 63 by using the above equation. Then, he sends 63 to a receiver. Subsequently, the receiver decodes 63 to get X which is actually 3 as the above proof indicates. Of course the receiver knows at least that the sender has used the above equation to get 63.
If the symbol mod is used, the equation X^13 = 85 x N + 63 can be expressed as X^13 = 63 mod 85. Then, you do not have to mind integers N, M, and L to solve the code.
In addition, a^(p - 1) = 1 (mod p)
or a^(p - 1) = K x p + 1
where a is an integer that cannot be divided by a prime number p while K is an integer. This formula is called Fermat's little theorem. This is used implicitly in the above solution of the equation. Specifically, the solution means X^(13 x 5) = 85 x A + 63^5, and X = 63^5. Because X^(13 x 5) - X = X x (X^[13 x 5 -1] -1) = 5 x B and 17 x C while 85 = 17 x 5. It is further because X^(13 x 5 -1) = 1 (mod 17) and 1 (mod 5), since 13 x 5 - 1 can be divided by the least common multiplier of 16 (= 17 - 1) and 4 (= 5 - 1), and then Fermat's little theorem a^(p - 1) = 1 (mod p) can be applied. (A and B are integers.)
What's more, the holy number 153 is related to the modern encryption system used in the Internet and PCc through Fermat's little theorem:
Joh 21:11 Simon Peter went up, and drew the net to land full of great fishes, an hundred and fifty and three: and for all there were so many, yet was not the net broken.153 is holy in that every integer that is a multiple of 3 is converted to 153 in a reasonable manner.
A slightly more obscure property of 153 is that it equals the sumHere. Fermat's little theorem: a^(p - 1) = K x p + 1 ---> a^p = J x p + a
of the cubes of its decimal digits. In fact, if we take ANY integer
multiple of 3, and add up the cubes of its decimal digits, then take
the result and sum the cubes of its digits, and so on, we invariably
end up with 153. For example, since the number 4713 is a multiple of
3, we can reach 153 by iteratively summing the cubes of the digits, as
follows:
starting number = 4713
4^3 + 7^3 + 1^3 + 3^3 = 435
4^3 + 3^3 + 5^3 = 216
2^3 + 1^3 + 6^3 = 225
2^3 + 2^3 + 5^3 = 141
1^3 + 4^3 + 1^3 = 66
6^3 + 6^3 = 432
4^3 + 3^3 + 2^3 = 99
9^3 + 9^3 = 1458
1^3 + 4^3 + 5^3 + 8^3 = 702
7^3 + 2^3 = 351
3^3 + 5^3 + 1^3 = 153
The fact that this works for any multiple of 3 is easy to prove. First, recall that any integer n is congruent modulo 3 to the sum of its decimaldigits (because the base 10 is congruent to 1 modulo 3). Then, letting f(n) denote the sum of the cubes of the decimal digits of n, by Fermat's little theorem it follows that f(n) is congruent to n modulo 3. Also, we can easily see that f(n) is less than n for all n greater than 1999. Hence, beginning with any multiple of 3, and iterating the function f(n), we must arrive at a multiple of 3 that is less than 1999. We can then show by inspection that every one of these reduces to 153.
http://www.mathpages.com/home/kmath463.htm
Then, a^3 = J x 3 + a
So, (a^3 + b^3 + c^3 + d^3 + ...) mod 3 = (a + b + c + d + ...) mod 3
while a + b + c + d + ... = I x 3
since n = a + 10 x b + 100 x c + 1000 x d + ... =
a + (9 + 1) x b + (99 + 1) x c + (999 + 1) x d + ... =
a + b + c + d +...+ 9 x (b + 11 x c + 111 x d + ...) =
H x 3.
(K, J, I, and H are all integers.)
Yes, it is Fermat's little theorem that links a modern encryption system used in the Internet and PCs to the Bible.
So, who wrote the Bible, selecting 153 so mysteriously in a passage describing a miracle performed by Christ Jesus?
Truly, this miracle has reached the Internet era 2000 years after the writing of the Bible.
In addition, the third party will find it difficult to see, say, 85 = 5 x 17 or division of 85 into primary numbers (p) if it is not simple 85 but a very big number. The difficulty lies in this factorization to prime numbers. For example, how can you know easily 99999640000243 = 9999973 x 9999991 without a computer? Even a PC cannot find an answer to a bigger number in short time, say, of a month or a week. So, this encryption method protects the secret message exchanged between a sender and a receiver from most of third parties.
To make sure, practically, after this factorization, the above (1) is followed to decide the power indexes of 13 and 5 (13 x 5 = L x 16 + 1) for the equation (X^13 = 85 x N + 63) and the solution (63^5/85).
SECTION II: 4000
Another holy number is 4000.
Mar 8:9 And they that had eaten were about four thousand: and he sent them away.
4000 is expressed as MMMM in a Roman numeral expression system.
As it is about four thousand, it might be 4032.
4032 = 1^3 + 2^3 + 3^3 + 5^3 + 7^3 + 11^3 + 13^3
= (1 x 1 x 1) + (2 x 2 x 2) + (3 x 3 x 3) + (5 x 5 x 5) + (7 x 7 x 7) + (11 x 11 x 11) + (13 x 13 x 13)
Note that 2, 3, 5, 7, 11, and 13 are all primary numbers.
In addition, the cube of a number, or especially a prime number, is important in Christianity as above proven.
Then, it must be like below.
This is the Cubic Cross.
*** *** *** ***
As I once wrote, when some 4000 people gathered to listen to Christ Jesus, each of them carried secretly some foods.
But, they were afraid of showing and sharing their foods with others, since there were so many people. So, each of them hid any bread or fish they had under the clothes or in bags.
Yet, as Christ Jesus started to show and share some bread and fish, they took out their hidden foods and started to eat them. Moreover, they even gave some to those who had little. This is truth of the miracle of Jesus' feeding 4000 people on a hill.
This is also a very important lesson, especially, for the U.S. Government and the American people of today.
(A Fukushima song...
http://d.hatena.ne.jp/haloouruma/20110715/1310720106)
Mar 8:1 In those days the multitude being very great, and having nothing to eat, Jesus called his disciples unto him, and saith unto them,
Mar 8:2 I have compassion on the multitude, because they have now been with me three days, and have nothing to eat:
Mar 8:3 And if I send them away fasting to their own houses, they will faint by the way: for divers of them came from far.
Mar 8:4 And his disciples answered him, From whence can a man satisfy these men with bread here in the wilderness?
Mar 8:5 And he asked them, How many loaves have ye? And they said, Seven.
Mar 8:6 And he commanded the people to sit down on the ground: and he took the seven loaves, and gave thanks, and brake, and gave to his disciples to set before them; and they did set them before the people.
Mar 8:7 And they had a few small fishes: and he blessed, and commanded to set them also before them.
Mar 8:8 So they did eat, and were filled: and they took up of the broken meat that was left seven baskets.
Mar 8:9 And they that had eaten were about four thousand: and he sent them away.