THEORY OF NUMBERS "Euclidean algorithm"

Euclidean algorithm is the algorithm to find the United Nations of two integers. Euclid, the inventor of the Euclidean algorithm is a Greek mathematician who wrote the algorithm in the famous book "Element".
Given two negative integers m and not n (m ≥ n). The following Euclidean algorithm to find the greatest common divisor of m and n.
Euclidean Algorithm 
1. If n = 0 then
m is the United Nations (m, n);
stop.
But if n ≠ 0
Proceed to step two:
2. Divide m by n and suppose that r is the remainder.
3. Change the value of m with the value and the value of n with r value, then reset back to step 1.
Example: m = 80, n = 12 and the filled condition m ≥ n

m = n. q + r
80 = 12.6 + 8
12 = 8. 1 + 4
8 = 4. 2 + 0
Time division last before 0 is 4, then the United Nations (80, 12) 4.
Theorem 1 (theorem Euclidean) such as m and n are two integers with the condition n> 0. If m divided by n then there are two unique integers q (quotient) and r (remainder), such that:

m = n. q + r
with 0 ≤ r ≤ n
example: (i) 1987 divided by 97 gives the results for the remaining 20 and 47.
1987 = 97. 20 + 47
(Ii) - 22 divided by 3 gives the results for - 8 and the remaining 2:
-22 = 3 (- 8) + 2
But - 22 = 3 (- 7) - 1 wrong, because r = - 1 are not eligible
0 ≤ r ≤ n.

MEANS OF PANCASILA

State philosophy Pancasila Indonesia is taken from Sanskrit which means five good behavior. Actually, the Pancasila doctrine itself has existed since long before the nation was formed Indonesia, Pancasila is the moral basis of teaching Buddhism, where the teaching is shared by followers of Siddhartha Gautama.
In Buddhism, the Pancasila reads as follows:
1. It will not be killing any living creature (human values)
2. Not going to take something that was given to him (equity value)
3. Not going to play man or woman (adultery is outrageous, family values)
4. Not going to lie (truth value)
5. Not be addicted to anything (exemption values)
While in Indonesia itself states represented in the Garuda Pancasila , which is used as a symbol of the state. This emblem was designed by Sultan Hamid II of Pontianak, and then perfected by President Sukarno.
The contents of Pancasila the basis for the Indonesian state philosophy:
1. Belief in God Almighty
2. Humanities Fair And Civilized
3. Persatuan Indonesia
4. Populist What Led by the wisdom of the Consultative / Representative
5. Social Justice For All People Indonesia

Symbol Meaning Garuda Indonesia
1. Middle of a defense shield Indonesia
2. Symbol - symbol in the shield of each - each representing the precepts - precepts of Pancasila are:
* Star symbolizes the principle of Belief in God Almighty
* The chain symbolizes humanity Fair And Civilized
* Banyan tree symbolizes the unity of Indonesia
* Head of the bull symbolizes the Populist Led by the wisdom of the Consultative / Representative
* Rice and cotton represent Social Justice For All People Indonesia
* The red and white Indonesian flag color symbolizes
* Thick black line across the shield symbolizes the Indonesian territory crossed the equator.
3. The number of feathers symbolizing the proclamation of Indonesian independence day 17 August 1945
* The number of feathers on each - each wing amounted to 17
* The number of feathers on the tail number 8
* The number of feathers under the shield / base of the tail number 19
* The number of hairs on the neck numbered 45
* Band is gripped by the bird Garuda Indonesia marked the state motto, which is Bhinneka Tunggal Ika, which means "different - different, but still one also.



sOURCE : salahketik.com