An Alternative Proof of Grand Problem II
Let me add to the story you read at the end of Chapter 2 an alternative solution to Grand Problem II.
Ivan V. Arzhantsev, a.k.a. Vania, is currently an associate professor in the Department of Higher Algebra at Moscow State University. I am looking at Vania’s original paper as I write these lines. It is (too) long andwitty. Its idea is, however, simple. Letme quote a concise version that belongs to the pen of the Russian problem-solving legend and de facto chair of the Soviet Union National Mathematical Olympiad (the formal chair was A. N. Kolmogorov), Nikolaj (Kolya) N. Vasiliev, who left us so untimely. Kolya writes in a June 28, 1990, letter to me (I am translating his letter from the Russian for you and adding references to the required parts of the first solution).