First slide

Introduction to P.M.I

Question

If $a, b, c, \in N, a^{n} + b^{n}$ is divisible by c when n is odd but not when n is even, then value of c is

Moderate

A

a + b
B

a – b
C

$a^{3} - b^{3}$
D

$a^{3} + b^{3}$

Solution

Use $a^{2 m + 1} + b^{2 m + 1}$
$\begin{aligned} = (a + b) (a^{2 m} - a^{2 m - 1} b + a^{2 m - 2} b^{2} - \dots - a b^{2 m - 1} + b^{2 m}] \end{aligned}$

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