Question

For what value of n 

x^n+y^n is exactly divisible by (x+y)?
 

Answer 1

let f(x,y) = x^n + y^n  ,is divisible by(x + y), so for f(x,y) = 0 at x + y = 0 ; or x = -y
{if any function is divisible by some function then this process do}
put x = -y in f(x,y),
f(x,-x) = x^n + (-x)^n = 0 -----------------------(1)
equation (1) is zero only for odd integer of value of n
hence for odd value of n  ,(x^n + y^n) is divisible by (x + y).