Which of the following is divisible by x 2 - y 2 ,   ∀   x ≠ y ?

Which of the following is divisible by x2-y2, ∀ x≠y?
  1. xn-yn ∀ n∈N
  2. xn+yn ∀ n∈N
  3. xn-ynx2n+1+y2n+1 ∀ n∈N
  4. xn-ynxm+ym ∀ m, n∈N

Solution

The expression xn-yn is divisible by (x+y)(x-y), if n=even.

Similarly, xn-yn is divisible by (x-y), if n=odd and
x2n+1+y2n+1 is divisible by (x+y).

Asked in: AP EAMCET 2019 (21 Apr Shift 2)

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