A former mathematics teacher from the “Al. I. Cuza” National College in Focșani managed to generalize a famous problem from the 1988 International Mathematical Olympiad – the same problem that the president of Romania, Nicușor Dan, solved with maximum score, obtaining a formula valid for a much wider range of mathematical situations.
Professor Mihai Teodor identified the underlying mathematical structure of the problem and performed a proof that provides all possible solutions for the parameters involved, recently published in the Online Encyclopedia of Integer Strings (OEIS), one of the most prestigious international mathematical databases.
The problem is also known for the fact that, at the 1988 edition, it was solved by the current president of Romania, Nicușor Dan. Professor Teodor confessed that he was inspired by the president’s account of how he found the solution.
“I saw a show where Mr. President told how he solved the problem: he tried several methods and finally came to a solution in five pages, in an hour and a quarter. I also thought about the problem and managed to solve it by another method. After I solved it, I asked myself if I could somehow find out all the values of the parameters for all the values of a and b, that is, the generalization of that problem.” said the teacher, quoted by Agerpres.
Through his method, the particular case of the International Olympiad now appears as a special example of a much more general result, representing a significant theoretical advance.
The professor points out that most of the existing sources presented only particular cases, easily obtained with the help of computers, but without a general formula.
“I looked on the Internet and in encyclopedias and nowhere did I find all the possible values presented. All kinds of particular cases appeared everywhere, which are obtained with the help of the computer very easily. I found that the general formula was missing, that is, the complete presentation of all solutions. That’s what I tried to do and I succeeded, the teacher stated. And the result is reusable and can be applied in solving equations with whole numbers, problems that are studied since middle school and up to the level high school and which appear frequently in mathematics competitions, proof that it was also given that year at the International Olympiad”says the teacher.
The 1988 problem was solved by only 11 participants, and the president’s elaborate solution was a complex one.
“Mr. President’s solution was a very elaborate one, but you have to take into account the context of the exam, where it’s important to reach the result. At that Olympiad, from all over the world, only 11 candidates managed to solve the problem, one of them being the president. I looked for a more concise solution and I managed to formulate it in one page”, Mihai Teodor also said.
His activity in mathematical research is not singular. In 2022, the professor published a formula for calculating the sum of products of all natural numbers up to a given number, confirming his constant contribution to the field.
Mihai Teodor retired last year, after over 30 years of activity at the “Al. I. Cuza” College in Focșani. Colleagues and former students appreciate his dedication and the results achieved throughout his career.
“Mr. Professor was an outstanding teacher. He prepared an impressive number of students for the baccalaureate, admission and Olympiads. Many of those who studied with him then attended important universities in the country and abroad“, said the director of the college, Andreea Săndulescu.
