If n is a natural number then 73n – 43n is always divisible by …(1 – InterviewSolution

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1.

If n is a natural number then 73n – 43n is always divisible by …(1) 11(2) 3 (3) 33 (4) both 11 and 3

Answer»

(4) both 11 and 3

7³ⁿ – 4³ⁿ is of the form a²ⁿ – b²ⁿ which is divisible by both a – b and a + b. So 7³ⁿ – 4³ⁿ is divisible by both 7 – 4 = 3 and 7 + 4 = 11.

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