$\forall n \in N; x^{2 n - 1} + y^{2 n - 1}$ is divisible by?

x - y

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x + y

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x y

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x^{2} + y^{2}

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Solution

The correct option is C $x + y$
$P (n) = x^{2 n - 1} + y^{2 n - 1} \forall n ϵ N .$
Substitute $n = 1$ to obtain $p (1) = x + y$ ,Which is divisible by $x + y$ .
For, $n = 2$ , we get $P (2) = x^{3} + y^{3} = (x + y) (x^{2} - x y + y^{2})$ which is divisible by $x + y$ .
With the help of induction we conclude that $P (n)$ will be divisible by $x + y$ for all $n \in N$ .
Ans: B

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Similar questions

Prove that $x^{2 n - 1} + y^{2 n - 1}$ is divisible by $x + y$ for all $n \in N$ .

n

\in

x^{2 n - 1} + y^{2 n - 1}

x^{2 n} - y^{2 n}

x + y

n \in N

P (n) = x^{2 n - 1} + y^{2 n - 1}

x + y

P (1)

P (k + 1)

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