
### Instruction: help me answer this question Is x2n – y2n divisible by x + y for all natural numbers, i.e., n?, think step by step
### Assistant: This can be proved using the principle of mathematical induction. For n=1, x2n – y2n = (x + y) (x – y), which is divisible by (x + y). Assuming P (k) to be true for some positive integer k, it can be shown that P (k + 1) is also true, hence P (n) is true for all natural numbers, i.e., n. , The answer is Yes, x2n – y2n is divisible by x + y for all natural numbers.
