proposition: Lemma lucas_pow2_odd n: odd (lucas (2^n)).
proof: Proof. elim: n => // n on; rewrite expn2S lucas_square'. case: n on=> // n. by rewrite {2} expn2S odd_double oddB ?lucas_powge2 // odd_sqr => ->. Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat) mathcomp(seq path fintype div bigop binomial) mathcomp(prime finset ssralg ssrnum ssrint)