xn – yn is divisible by (x – y) when n is ……………. A) a p

1.	xn – yn is divisible by (x – y) when n is ……………. A) a prime number B) an odd number C) an even number D) a natural number
Answer» Correct option is (D) a natural number \(x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y\) \(+x^{n-3}y^2+....+xy^{n-2}+y^{n-1}),\) where n is a natural number. Thus, \(x^n-y^n\) is divisible by x - y when n is a natural number. Correct option is D) a natural number

xn – yn is divisible by (x – y) when n is ……………. A) a prime number B) an odd number C) an even number D) a natural number

Answer»

Correct option is (D) a natural number

\(x^n-y^n=(x-y)(x^{n-1}+x^{n-2}y\) \(+x^{n-3}y^2+....+xy^{n-2}+y^{n-1}),\) where n is a natural number.

Thus, \(x^n-y^n\) is divisible by x - y when n is a natural number.

Correct option is D) a natural number