If n is a natural number- then 92 n-42 n is always divisible bya 5b 13c both 5 and 13d None of these-Hint - 92 n-42 n is of the form a2 n-b2 n which is divisible by both a-b and a-b- So- 92 n-42 n is divisible by both 9-4-5 and 9-4-13-

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Factors of Natural Numbers

If n is a nat...

Question

If n is a natural number, then 9²ⁿ − 4²ⁿ is always divisible by

(a) 5
(b) 13
(c) both 5 and 13
(d) None of these

[Hint : 9²ⁿ − 4²ⁿ is of the form a²ⁿ − b²ⁿ which is divisible by both a − b and a + b. So, 9²ⁿ − 4²ⁿ is divisible by both 9 − 4 = 5 and 9 + 4 = 13.]

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