There is a statement recently published in the author's note:
Quote:For this complex equation with natural variables (distinct and greater than one), there is no general algorithm to prove or disprove the existence of a solution, except by complete enumeration. Moreover, attempting to prove that no such algorithm exists, as well as attempting to prove this statement, will prove more difficult than simply performing the enumeration.
Quote:k ^ n * (a^n + b^m) / (n ^ a + c) = n^k * sin(m ^ n + b ^ a) / (m ^ a - c),
where a, b, c, n, m, k ∈ N, a, b, c, n, m, k > 1, and a ≠ b ≠ c ≠ n ≠ m ≠ k.
[Hypothesis on the Equation of Impossibility [Van B. Petrov], 2025, (published only in Russian)]
I wonder how true this statement is and how one could try to prove or disprove it? As I understand it, this is essentially a type of Diophantine equation?
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