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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