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Which of the following numbers exactly divides $(4 9^{15} - 1)$ ?

Competition practiceNumber System, HCF & LCM

A14
B50
C51
D8

Step-by-Step Solution

x^{n} - a^{n}

is always divisible by

x - a : 49 - 1 = 48

, hence by 8. It is divisible by

x + a = 50

only for even

n

, and 15 is odd.

Answer: D) 8

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