On some analogs of Eminyan’s problem

In 1996, K.M.Eminyan found an asymptotic formula for the number of solutions of the equation $n-m=1$ in variables $n$ and $m$ with given parity of the sums of binary expression digits. In 2020, the speaker found an asymptotic for the similar problem where the binary expressions are replaced by Fibonacci coding. In the talk, we will speak about further generalizations of this result.