If n is an odd positive integer, then a^n + b^n is divisible by: - Vidyadip

MCQ

If $n$ is an odd positive integer, then $a^n + b^n$ is divisible by:

A
$a^2 + b^2$
✓
$a + b$
C
$a – b$
D
none of these

✓

Answer

Correct option: B.

$a + b$

Given number $= a^n + b^n$
Let $n = 1, 3, 5, ……..$
$a^n + b^n = a + b$
$a^n + b^n = a^3 + b^3 = (a + b) \times (a^2 + b^2 + ab)$ and so on.
Since, all these numbers are divisible by $(a + b)$ for $n = 1, 3, 5,…..$
So, the given number is divisible by $(a + b)$

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