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Q.

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

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a

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

b

a – b

c

a + b

d

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

answer is A.

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Detailed 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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If a,b,c,∈N,an+bn is divisible by c when n is odd but not when n is even, then value of c is