Question

find whether xⁿ+yⁿis divisible by x-y (y≠0)
or not. please give answer in short​

Answer 1

Let P(n) denote the statement

is divisible by x-y

put n=1,

P(1): x - y is divisible by x-y

Assume the result is true for n=k

That is, is divisible by x-y

where c is an integer

To prove P(k+1) is true

That is to prove:

is divisible by x-y

, is divisible by x-y

Therefore P(k+1) is true

Hence by mathematical induction P(n) is true for all natural numbers

Answer 2

Answer:

Yes

Step-by-step explanation:

Let x be 4, y be 2 and n be 3

4^3=64

2^3=8

64+8=72

4-2=2

72 is divisible by 2

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