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Question

nN;x2n1+y2n1 is divisible by?

A
xy
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B
x+y
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C
xy
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D
x2+y2
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Solution

The correct option is C x+y
P(n)=x2n1+y2n1nϵN.
Substitute n=1 to obtain p(1)=x+y ,Which is divisible by x+y.
For, n=2, we get P(2)=x3+y3=(x+y)(x2xy+y2) which is divisible by x+y.
With the help of induction we conclude that P(n) will be divisible by x+y for all nN.
Ans: B

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