Q. The number $a^{n} - b^{n}(a,b$ are distinct rational numbers and $n \in N$) is always divisible by
A) $a - b$
B) $a + b$
C) $2a - b$
D) $a - 2b$
Explanation
(a)
Let $P(n) \equiv a^{n} - b^{n}$
$P(1) \equiv a - b$
$P(2) \equiv a^{2} - b^{2}$
Hence, it is divisible by $a - b$.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.