Q. If $x^{2n - 1} + y^{2n - 1}$ is divisible by $x + y$, if $n$ is
A) A positive integer
B) An even positive integer
C) An odd positive integer
D) None of the above
Explanation
(a)
Let $P(n\ ) \equiv x^{2n - 1} + y^{2n - 1} = \lambda(x + y)$
$P(1) \equiv x + y = \lambda_{1}(x + y)$
$P(2) \equiv x^{3} + y^{3} = \lambda_{2}(x + y)$
Hence, for $\forall\ n \in N,\ P(n)$ is true.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.