The sequence (an)n≥1 is defined by a_1 \equal{} 3, a_2 \equal{} 11 and a_n \equal{} 4a_{n\minus{}1}\minus{}a_{n\minus{}2}, for n≥3. Prove that each term of this sequence is of the form a^2 \plus{} 2b^2 for some natural numbers a and b. inductionquadraticsnumber theoryalgebra proposedalgebra