# Q) What is the greatest common divisor of ${3}^{{3}^{333}}+1$ and ${3}^{{3}^{334}}+1?$

ans;4

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3^334 =3^(333+1) = 3^333*3^1  =3^333*3 =3^(333*3)=3^333^3

so 3^3^334 + 1 = 3^3^333^3 + 1 =( 3^3^333 + 1)( (3^3^333)^2 - 3^3^333 + 1) # h^3 +1 = (h+1)(h^2 -h +1)
thus 3^3^333 + 1 is a factor of 3^3^334 + 1
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