Rs discussed in Chapter . Euler was the rst to fruitfuy extend any of Fermat's signicant work in number theory. That is the case here as well. Instead of using brute force to try to nd factors of F5, Euler ingeniously eliminated the majority of potential factors by analysing properties potentially successful divisors would be required to have. In particular, he showed that if F5 was not prime it must have a prime factor of the form 54k + 1 where I: is a positive integer. 33. Compute the numbers dls: + 1 for I: = 1,,2I ... I1|]