Abstract
In [SS1] Schlickewei and Schmidt studied the solutions of various linear equations involving members of recurrence sequences. Most of them are of the form $$ F_1 \left( {x_1 } \right) + \cdots + F_n \left( {x_n } \right) = 0 $$ (A) with x i ∈ ℤ, where \( F_j \left( x \right) = \sum\nolimits_{i = 0}^{r_j } {f_{ji} \left( x \right)\alpha _{ji}^x \left( {j = 1, \ldots ,n} \right)} \), r j > 0 with given polynomials f ji and nonzero numbers αji (thus for each j, (F j (x))x∈ℤ is a linear recurrence sequence, see also [ST, Sec.C]). The general assumption of [SS1, p.220] is that αj0 is a root of unity and that f ji ≠ 0 for i > 0 (f j0 may be zero), j = 1, ..., n. Furthermore, they restrict to nondegenerate sequences, i.e., αji/αjh is not a root of unity for h ≠ i.
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