Question 73

Which of the following numbers will completely divide $$7^{81} + 7^{82} + 7^{83}$$ ?

Solution

$$7^{81} + 7^{82} + 7^{83}$$ = $$7^{80}\left(7+7^2+7^3\right)$$

= $$7^{80}\left(7+49+343\right)$$

= $$7^{80}\left(399\right)$$

= $$399\left(7^{80}\right)$$

$$\therefore\ $$399 completely divides the $$7^{81} + 7^{82} + 7^{83}$$

Hence, the correct answer is Option B

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