Statement 1: For each natural number n, (n+1)^7-n^7-1 is divisible by 7. Statement 2: For each natural number n, n^7-n is divisible by 7.

JEE Main Mathematics question

Not in JEE syllabus

Statement 1: For each natural number , is divisible by . Statement 2: For each natural number , is divisible by .

(A)Assertion is True, Reason is True; Reason is correct explanation for AssertionCorrect
(B)Assertion is True, Reason is True; Reason is not correct explanation for Assertion
(C)Assertion is True, Reason is False
(D)Assertion is False, Reason is True

Answer: (A)

Solution

Statement 2 is true: is divisible by (Fermat's little theorem; or and the binomial theorem). Statement 1 follows from it: , a difference of two multiples of , so it is

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Question ID VK-021286