x^ 3^n +y^ 3^n is divisible by x+y if

JEE Advanced Mathematics question

is divisible by if

(A) is any integer Correct
(B) is an odd positive integer
(C) is an even positive integer
(D) is a rational number

Answer: (A)

Solution

is divisible by iff putting gives zero, i.e. , which happens iff is an odd positive integer. Here , and is an odd positive integer for **every** integer (including

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Question ID VK-107897