proposition: Lemma fib_is_even_mod3 n: odd (fib n) = (n %%3 !=0).
proof: Proof. move: (gcd_fib n 3); rewrite - (gcdn_modl n) gcd_n2. move:(mod3_small n);case:(n %% 3) => [|[|[| k]]] //= _; case: odd => //. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)