One combinatorial inequality (Q5960273)

The author proposes a new proof of the result on the best estimate from below of the linear form \(\Lambda = b_2\log \alpha_2 - b_1\log \alpha_1\), where \(\alpha_1\) and \(\alpha_2\) are the algebraic numbers and \(b_j\in \mathbb Z \) are the integer coefficients. The estimate was obtained by P. Voutier [see \textit{M. Laurent, M. Mignotte} and \textit{Yu. V. Nesterenko}, J. Number Theory 55, No. 2, 285-321 (1995; Zbl 0843.11036)].