Lemma. If F₆ = {0, 1, a, a², a³, a⁴} is a field, then there exists some xin{1, a, a², a³, a⁴} s.t. x + x = 0.
Prove the following lemma.
Lemma. If F₆ = {0, 1, a, a², a³, a⁴} is a field, then for any yin{1,a, a², a³, a⁴}, y + y = 0.