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प्रश्न
If n is a natural number, then 92n − 42n is always divisible by ______.
पर्याय
5
13
both 5 and 13
None of these
उत्तर
If n is a natural number, then 92n − 42n is always divisible by both 5 and 13.
Explanation:
Given, 92n − 42n is in the form of a2n − b2n where n is a natural number.
Since a2n − b2n is always divisible by (a − b) and (a + b),
92n − 42n is always divisible by:
9 − 4 = 5
9 + 4 = 13
∴ 92n − 42n is always divisible by both 5 and 13.
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