Remainders of Continuants with Large Fixed Suffixes

To every finite word of a finite alphabet A⊆ N , one can add a prefix V and a suffix W that are fixed finite words of the alphabet N . The words thus obtained are related to finite continued fraction expansions of certain numbers from (0,1)∩ Q . Their irreducible denominators that belong to $$[1,N]$$ form the set DNA,V,W . In the author’s previous work, it was shown that, under certain conditions on A and Q , and provided that the lengths of V and W are not very large, the set DNA,V,W contains almost all possible remainders modulo Q ; moreover, the corresponding formula has power-law decay. In this paper, we obtain an analogous formula for an arbitrarily long suffix W .