Question
Download Solution PDFWhich of the following numbers is a divisor of \((49^{15} - 1) \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\((49^{15} - 1) \)
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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