Question 107

$$4^{61} + 4^{62} + 4^{63} + 4^{64}$$ is divisible by

Solution

$$4^{61} + 4^{62} + 4^{63} + 4^{64}$$

Taking $$4^{61}$$ common from the above expression, we get :

=> $$4^{61}$$ ($$4^{0}$$ + $$4^{1}$$ + $$4^{2}$$ + $$4^{3}$$)

=> $$4^{61}$$ (1 + 4 + 16 + 64) = $$4^{61}$$ * 85

$$\because$$ 85 is divisible by 17

=> $$4^{61} + 4^{62} + 4^{63} + 4^{64}$$ is divisible by 17

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