Value of m∈N for which xm+ym is divisible by x+y. Let P(m)=xm+ym 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):x2+y2 is divisible by x+y which not true ⇒P(2) is not true. ⇒m=3 ⇒P(3)=x3+y3 is divisible by x+y. ∴x3+y3=(x+y)(x2−xy+y2) ∴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 notvalid) Option 4 Only when m=1 wrong because valid for m=3 it is possible.