Chapter Forty-Nine: Heartache

“The largest integer k such that 10 to the power of k divides 199 factorial.”
Wu Tong read the problem carefully and formed a plan. It wasn’t a tricky or convoluted question; the intent was clear.
Wu Tong took the pen from Teacher Li and continued writing the solution on the scratch paper. According to Theorem 3, the exponent of 5 in the prime factorization of 199! is..., while the largest integer K for 2 is 47, ...
“So, the largest integer we’re seeking is K equals 47, Teacher Li!” Wu Tong looked at Li Yisheng and, without hesitation, gave her answer.
Li Yisheng’s eyes shone even brighter than Teacher Zhou from the admissions office the moment Wu Tong answered. His excitement nearly burst through the walls and finally turned into a deep sigh.
“It’s such a pity, teacher, to have met you only now. If you’re willing, I invite you to begin your studies at Jing University right away. The mathematics department at Jing University welcomes you!”
“Teacher Zhou, this is a graduate-level mathematics exam question. Wu Tong’s solution is concise, clear, and absolutely correct!”
“University-level mathematics—Wu Tong has mastered it thoroughly! Her academic level is almost equivalent to a Jing University graduate student. To keep such a gifted student trapped in a small county high school with limited educational resources, endlessly grinding through repetitive exercises, is a true waste of talent!”
It pained him deeply!
With scarce resources and limited textbooks, she had managed to learn this much through self-study. Her talent and ability to learn were breathtaking!
If she had grown up in a resource-rich educational environment, if they had encountered her earlier, just how dazzling her growth would have been!
Fortunately, she was only sixteen, and they had the good fortune to meet her! As long as she continued to grow, he would not be surprised if she surpassed his own achievements and became a shining star of Jing University.
Professor Li pointed to a few of the accompanying student representatives who had gathered to watch. “Just look at the expressions on these slackers’ faces, and you’ll know Wu Tong’s level!”

“Heh heh...” The senior students smiled sheepishly. “Please don’t compare us, teacher, we’re just ordinary students struggling to survive!”
They knew they were in no position to be compared to such a prodigy, even one for whom the university would offer a million-yuan prize.
“Teacher Li, you flatter me. Mathematics is vast and profound; I’m only circling the threshold and haven’t fully entered. I haven’t seen all the university textbooks yet, and there are still things I haven’t learned or mastered. I still need to keep studying!” Wu Tong replied modestly, feeling a bit embarrassed. Their fields of study were different; it wasn’t fair to compare herself to the seniors.
“The way the seniors handle themselves and their attention to detail is something I need to learn from!” Since she had just benefited from their care, she couldn’t let her seniors lose face.
Hearing this, the student representatives immediately shot grateful glances at their future junior. What a considerate person!
“When you get back, pay extra attention to your advanced calculus,” Li Yisheng warned, casting a sharp look at the relieved students, as if to say, “Just you wait.”
The signing was the priority. Without further delay, with the parents and Coach Zhang as witnesses, Wu Tong formally signed her name on the final agreement prepared by Jing University’s admissions office, confirming her plan to start early studies at Jing University after the new year.
“Jin Xin, would you like to come study at Jing University as well? Your grades are quite good—why not join Wu Tong?” With the signing done, the atmosphere relaxed, and Teacher Zhou began chatting with the Jin and Wu families.
He knew that over the past few months, Wu Tong had been tutoring Jin Xin, whose grades had soared—now over 660, especially in mathematics and science, consistently above 140 and 280, respectively. Smiling, he extended the invitation.
With those scores, Jin Xin was very close to Jing University’s admission threshold, especially in mathematics and science, where she excelled. With Wu Tong as a strong supporter and tutor, her college entrance exam results would surely surprise everyone. Bundling them together was a win for the university.
“Heh heh... Jing University used to be a goal agreed upon by Tong Tong and me, but now I’ve chosen my path—I want to apply to a military academy!” Jin Xin scratched her head, a little embarrassed. If it had been at the start of senior year, she would have agreed wholeheartedly, but now she didn’t want to take advantage of Tong Tong’s achievements.
“Applying to a military academy? Great ambition! I wish you a bright future!” Teacher Zhou applauded, praising them. What an incredible family—both children had clear goals and worked tirelessly towards them. It was truly admirable!
After the signing, Teacher Zhou thoughtfully arranged a late-night meal, inviting the rest of the Central Plains provincial team in the spirit of recruiting more talent, and promoted Jing University to the remaining team members.

This year, the Central Plains provincial team performed well; aside from Wu Tong’s unprecedented perfect score and first place in the CMO, there were two other national gold medalists. Among them, a girl named Feng Yueyue scored 87, surpassing the national training team threshold and qualifying for the national training camp. This meant that Central Plains would send two students to the national training camp this year—a great achievement, making Coach Zhang Ping and Teacher Zhang very happy.
Teacher Zhou was also delighted. He finalized an agreement with Feng Yueyue, who ranked second in Central Plains and 30th in the CMO, for direct admission to the mathematics department at Jing University, as well as with another national gold medalist for entry into Jing University’s top foundation program.
“I’ll send you some textbooks soon. Take your time reading through them, and if you have any questions, you can ask me anytime. When you come to Jing University, we can discuss things together.” Before Wu Tong returned to her room, Professor Li handed her a copy of Analytical Number Theory that he carried with him, urging her to study. His own research leaned toward functional analysis, but he studied number theory for interdisciplinary purposes, and just happened to have this book on hand for Wu Tong.
He felt so sorry for such an extraordinary student, unable to continue learning just because she couldn’t borrow the necessary textbooks!
“Thank you, Teacher Li. See you at Jing University after the New Year—I’ll come wish you a happy New Year!” It was true that the small county couldn’t provide her with more resources, and with national team training after the holidays, Wu Tong had decided to head to the capital at the start of the year.
This year, the IMO national training camp would be held in Jiangcheng. According to Teacher Li’s advance notice, their cohort would be directly recruited by Jing University for training next year. She could go early, and the university would arrange everything for her academic life.
The next day at nine o’clock, the awards ceremony for the twenty-fourth Chinese Mathematical Olympiad was held. With the Chinese Mathematical Society presiding over the event, the awards were presented with great ceremony.
As this was an odd-numbered year, the problem-setting committee had further increased the difficulty, resulting in an unprecedentedly low threshold for the national first prize. The national first prize cutoff was set at 66, and the national training team at 75.
This year, a total of forty-two national first prizes and thirty national training team members were awarded. The second prize cutoff was 50; the third prize was not tallied, as simply qualifying for the national competition was considered a consolation prize in itself.
When the news reached the Central Plains, the education community there was filled with joy.