In this paper we prove that all solutions (y,m,n) of the equation 3m − 2yn = ±1, y,m,n ∈ N, y > 1, m > 1, n > 1, satisfy y < 106⋅109 , m < 1,4 ⋅ 1015 and n < 1,2 ⋅ 105.
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