Discussion Forum



1)

$x^{n}+y^{n}$  is divisible by 


A) x-y for all $n\in N$

B) x+y for all $n\in N$

C) x+y for all n=2m-1 , $m\in N$

D) x+y for all n=2m, $m\in N$

Answer:

Option C

Explanation:

Given , $x^{n}+y^{n}$

 at n=1,x+y , which is divisible by x+y

 n=2, $x^{2}+y^{2}$, which is  not divisble by x+y

n=3, $x^{3}+y^{3}$ ,  which is divisble  by x+y

 Hence, clearly $x^{n}+y^{n}$ is divisble by n= odd numbers  as n=2m-1 , where   $M \in  N$.