Meng Zhao picked up his brush and gently drew an "x" on the Xuan paper. Zhuge Fuzi, who was standing next to him, asked, "This symbol looks like the multiplication sign we've seen before."
“They are indeed somewhat similar, but there are still many differences when writing them.” Meng Zhao then picked a blank space and wrote the letter x and the multiplication sign. “The multiplication sign is two straight lines intersecting, while the lines of the x are more elegant and graceful. If you are worried that it will be difficult to recognize when writing, you can replace the multiplication sign with a dot.”
Then, she wrote the congruence sign ≡ on the paper. "This symbol is called the congruence sign. It looks a bit like the equal sign you've seen before, but it's not the same. The equal sign means that the values on both sides are completely equal, while the congruence sign means that the values on both sides are equal only under certain rules."
"By learning these two symbols, we can replace the originally complicated problems with simple formulas. The remainder after counting threes is x≡2 (mod 3)."
"Madam Meng, what...what, 'mo' do you mean?" The person who asked the question was about thirty years old, one of the younger people present. Even though the person was standing slightly relaxed, his right hand was still clenched into a fist in front of him, his feet were slightly apart and level with his shoulders, and with his slightly straight back and rough voice, Meng Zhao guessed that this person must know martial arts.
"mod means to find the remainder after dividing two numbers. Its core concept is 'modulo 3', such as 7 modulo 3, which means 7 divided by 3 leaves a remainder of 1."
After explaining the meaning of these symbols, Meng Zhao then tried to rephrase the remaining theorems in language that the ancients could understand. The people present sometimes frowned in thought, and sometimes suddenly realized, all of them immersed in the problem.
"...Therefore, the final solution can be expressed as x ≡ 23 mod 105, which means the smallest answer is 23, and subsequent answers are multiples of 23 plus 105, such as 128, 233, 338."
When she finished writing, the room fell silent and no one responded. Meng Zhao could only look at Dean Gu, the eldest among them.
Meanwhile, everyone else present turned their gazes to Dean Gu. Dean Gu glanced at the others one by one, his silver beard trembling slightly as he said, "Um... Madam Meng, could you say it again?"
Hearing him say that, the others breathed a sigh of relief. Thank goodness, they weren't the only ones who didn't understand. They then said in succession, "Yes, Madam Meng, please say it again. Just now you mentioned something about equal addition and subtraction, and I really didn't follow your train of thought."
Meng Zhao wondered what had happened, but when she realized it was like this, she replied gently, "Of course, I have already made arrangements for things today, and there is plenty of time."
So Meng Zhao first asked everyone what they didn't understand, and based on everyone's questions, he focused on explaining those points during the second explanation.
After the explanation was given twice, some people had already grasped the basics. "I think I understand a little, but I still need to explore it a few more times."
Dean Gu looked intently at Meng Zhao, "Wonderful! Wonderful! The problem that has troubled us for many years has been solved today thanks to Madam Meng. We are truly grateful to Madam Meng." After saying this, he bowed to Meng Zhao.
Meng Zhao quickly waved his hand and took two steps back. "Dean Gu, you flatter me. I'm just standing on the shoulders of giants and have only learned a few things by chance. Today we're just discussing things with each other, so there's really no need for thanks." If anyone should be thanked, it should be for compulsory education. Otherwise, as an orphan, Meng Zhao might not have been able to learn these things.
At this moment, someone spoke up: "But isn't this algorithm too convoluted? It doesn't seem to be much faster than our old method."
The man who spoke was thin, and the collar and cuffs of his cotton robe were slightly frayed, indicating that it had been washed many times. Judging from his words and actions, Meng Zhao thought he was a scholar.
Master Zhuge, standing to the side, said, "This is naturally different. In the past, when we encountered this kind of problem, we would try one number at a time, but now we have this... this..."
"The formula," Meng Zhao reminded him at the opportune moment.
"Yes! With this formula, it will naturally be simpler."
Meng Zhao's eyes lit up, and he suggested, "How about this, let's have a competition right here. One person will pose a question, and the rest of us will solve it. Let's see if the old exhaustive search method or the formula is faster, shall we?"
As soon as the suggestion was made, the others responded enthusiastically, "Okay, let's do it that way. Let's have a competition to see which method is better."
The straightforward man in the indigo robe volunteered, "Then I'll ask the questions, and you can answer them."
After everyone nodded in agreement, he walked around the courtyard a few times and then said, "When the general is counting his soldiers, there are 2 soldiers left over if there are 3 soldiers in each rank; 1 soldier left over if there are 4 soldiers in each rank; 3 soldiers left over if there are 5 soldiers in each rank; 5 soldiers left over if there are 6 soldiers in each rank; and 4 soldiers left over if there are 7 soldiers in each rank. What is the minimum number of soldiers in this rank?"
As soon as the questions were heard, someone began to complain: "Song Siye, do you know you don't need to answer, so you're deliberately making things difficult for us? How can you do this? There were three questions before, but now there are five."
Upon hearing the title "Director of Studies," Meng Zhao couldn't help but glance at the man a couple more times. He laughed loudly, "Since we're going to have a competition, we can't use easy questions." After saying that, he looked at the reactions of the others and reminded them, "I advise you not to complain. Look, Dean Gu has already started writing."
The man then realized what was happening, turned his head, and saw that they had already started calculating. So he hurriedly picked up his pen as well.
When they were talking earlier, Meng Zhao had noticed their clothing and appearance. Some people wore jade ornaments, which were obviously the finest jade. Others were dressed simply, and their clothes had been washed many times. However, when they discussed arithmetic problems, everyone spoke their minds.
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