Linear recurrence sequences satisfying congruence conditions
Linear recurrence sequences satisfying congruence conditions
It is well-known that there exist integer linear recurrence sequences $\{x_n\}$ such that $x_p \equiv x_1$ (mod $p$) for all primes $p$. It is less well-known, but still classical, that there exist such sequences satisfying the stronger condition $x_{p^n} \equiv x_{p^{n-1}}$ (mod $p^n$) for all primes $p$ and $n \ge …