Which of the following numbers is a divisor of \((49^{15} - 1) \)?

This question was previously asked in
SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 1)
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  1. 46
  2. 14
  3. 8
  4. 50

Answer (Detailed Solution Below)

Option 3 : 8
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Detailed Solution

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Given:

\((49^{15} - 1) \)

Concept used:

an​​​​​​ - bn is divisible by (a + b) when n is an even positive integer.

Here, a & b should be prime number.

Calculation:

\((49^{15} - 1) \)

⇒ \(({(7^2)}^{15} - 1) \)

⇒ \((7^{30} - 1) \)

Here, 30 is a positive integer.

​According to the concept,

\((7^{30} - 1) \) is divisible by (7 + 1) i.e., 8.

∴ 8 is a divisor of \((49^{15} - 1) \).

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