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Conjecture on the unsolvability of the $\{3 \times 3 \times \cdots \times 3\} \subseteq \mathbb{R}^k$ dots problem starting from the central point

In 2020 (see Solving the $106$ years old $3^k$ points problem with the clockwise-algorithm, JFMA, 3(2), p. 96), I conjectured that, in the Euclidean space $\mathbb{R}^k$, we can cover any given set of ...
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Is the conjecture A+B=C following correct?

Is the conjecture on A+B=C following correct ? Conjecture: Let $A, B, C$ be three positive integer numbers such that $A+B=C$ with $\gcd(A, B, C) = 1$. By Fundamental theorem of arithmetic we write: $...