The Chinese Remainder Problem

The Chinese Remainder Problem
Nihar Baddigam
Background information The Chinese remainder problem is a mathematical problem first proposed by the brilliant strategist and capable mathematician, Sun Tzu. The theorem used to solve the problem was born out of necessity, as the Chinese calendar was not fixed, but instead varied based on the phases of the moon. Sun Tzu provides this question in a book of problems. The math behind the problem was already well established in China, as identifying the dates on which multiple natural phenomena (such as full moons or the winter solstice) occurred simultaneously was fundamental to the Chinese calendar. The exact wording of the problem, after translation is as follows-
“There are certain things whose

In addition I will aim to use a more developed theorem to solve a hypothetical real life situation.

Personal relevance The Chinese remainder problem is, to me, an example of how even the simplest of mathematical problems can have quite a bit of understanding required to master them. The problem initially seemed deceptively simple, but proved to be impossible for me to solve when I initially attempted it. Learning the concept of the modulus and understanding the simple logic that was used to concoct an answer to this problem, I was surprised by the simplicity of the problem once the mathematical logic was revealed.

Having read "The Art of War" by Sun Tzu, I was curious to learn that he was also a profound mathematician. This seemingly simple puzzle intrigued me, as I wasn't sure what made it such an important problem. I had seen similar questions in other math textbooks, and I strongly desired to be able to solve such problems, and understand the mathematical knowledge behind

This function will be expressed hereafter in a form similar to this: x≡a (mod y). This is held to have the same meaning as “when x is divided by y, the remainder is y”. The ‘≡’ symbol means “congruent” or “equivalent”, and is used to show the relationships between numbers in the system.

Beginning with the first condition, we can write the condition using the modulus function as: x≡2(mod 3);
Keeping in mind that only whole numbers can be accepted as answers, we can deduce a sequence of numbers for which the above condition is true, of which any value could be the value of x:
2,5,8,11,14,17,20,23…
We can see that this sequence has a general term defined as shown below.
Un=3n-1;
The second condition can be defined as: x≡3(mod 5);
Again, we can deduce a sequence of numbers for which this condition is true:
3, 8, 13, 18, 23…
The formula for the general term of this series is:
Un=5n-2;
The number 8 satisfies both conditions, and hence will be the starting point for finding a number that satisfies the third condition. Here I observed an interesting