On the size of a linear combination of two linear recurrence sequences over function fields

Abstract Let $$ G_n G n and H_m H m be two non-degenerate linear recurrence sequences defined over a function field F in one variable \mathbb {C}$$ C , let \mu μ valuation on . We prove that under suitable conditions there are effectively computable constants c_1 c 1 C' ′ such the bound $$\begin{aligned} (G_n - H_m) \le (G_n) + \end{aligned}$$ ( - ) ≤ + holds for \max \left( n,m \right) > max , >