Let α and β be the roots of the quadratic equation x2+mx−1=0, where m is an odd integer. Let λn=αn+βn, for n≥0. Prove that for n≥0. (a) λn is an integer; and (b) GCD(λn,λn+1)=1

Let α and β be the roots of the quadratic equation x2+mx−1=0, wher

1.	Let α and β be the roots of the quadratic equation x2+mx−1=0, where m is an odd integer. Let λn=αn+βn, for n≥0. Prove that for n≥0. (a) λn is an integer; and (b) GCD(λn,λn+1)=1
Answer» Let $α a n d β$ be the roots of the quadratic equation $x^{2} + m x - 1 = 0$ , where m is an odd integer. Let $λ_{n} = α^{n} + β^{n}$ , for $n \geq 0$ . Prove that for $n \geq 0$ . (a) $λ_{n}$ is an integer; and (b) $G C D (λ_{n}, λ_{n + 1}) = 1$

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Let α and β be the roots of the quadratic equation x2+mx−1=0, where m is an odd integer. Let λn=αn+βn, for n≥0. Prove that for n≥0. (a) λn is an integer; and (b) GCD(λn,λn+1)=1

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