A necessary and sufficient condition ("nonresonance") is established forevery solution of an autonomous linear difference equation, or more generallyfor every sequence $(x^\top A^n y)$ with $x,y\in \mathbb{R}^d$ and $A\in\mathbb{R}^{d\times d}$, to be either trivial or else conform to a strong formof Benford's Law (logarithmic distribution of significands). This conditioncontains all pertinent results in the literature as special cases. Itsnumber-theoretical implications are discussed in the context of specificexamples, and so are its possible extensions and modifications.
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机译：为自治线性差分方程的每个解决方案建立一个必要和充分的条件（“非共振”），或更普遍地，对于\ mathbb {R} ^中的每个带有$ x，y的序列$（x ^ \ top A ^ ny）$ d $和$ A \ in \ mathbb {R} ^ {d \ times d} $，要么微不足道，要么符合本福德定律的强形式（对数的对数分布）。这种情况包含特殊情况下文献中的所有相关结果。在具体示例的上下文中讨论了其理论意义，以及可能的扩展和修改。
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