For what values of m N , the following divisibility x+y / x^m+y^m holds?

Step-by-step solution

Value of m N for which x^m+y^m is divisible by x+y . Let P(m)=x^m+y^m is divisible by x+y . Let us consider m=1 . P(1): x+y is divisible by x+y ; P(1) is true m=2 P(2): x^2+y^2 is divisible by x+y which not true P(2) is not true. m=3 P(3)=x^3+y^3 is divisible by x+y . x^3+y^3=(x+y) (x^2-x y+y^2 ) P(3) is true. Option 1 Even number wrong ( m=2 not valid). Option 2 odd number right. Option 3 All natural number wrong ( m=2 not valid) Option 4 Only when m=1 wrong because valid for m=3 it is possible.