Question 1073095
<pre>
{{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", (3^((3^334))+1))}}} 

 {{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", (3^((3^(333+1)))+1))}}}

 {{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", (3^((3^333*3^1))+1))}}}

 {{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", (3^((3^333*3))+1))}}}

 {{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", ((3^((3^333)))^3+1))}}}

Factor the second one as the sum of two cubes

 {{{matrix(2,5,"","","","","",GCD, of, (3^((3^333))+1), "&", (3^((3^333))+1))((3^((3^333)))^2-3^((3^333))+1))}}}

Since the first one is a factor of the second one, the
greatest common factor is the first one:

 {{{matrix(2,1,"",(3^((3^333))+1))}}}

Edwin</pre>