Question 139

The greatest common divisor of $$3^{3^{333}}+1$$ and $$3^{3^{334}}+1$$ is :

Solution

Let $$X$$ = $$3^{3^{333}}+1$$

=> $$X-1$$ = $$3^{3^{333}}$$

Let $$Y$$ = $$3^{3^{334}}+1$$

$$Y-1$$ = $$3^{3^{334}}$$

$$Y-1$$ = $$(3^{3^{333}})^{3}$$

=> $$(Y-1) = (X-1)^{3}$$

On expanding, The 1s on both sides will get cancelled. Y can be represented in terms of X. This clearly indicates that X is a factor of Y.

Therefore, the HCF is $$3^{3^{333}}+1$$

Option C is the right answer.

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