A note on factorization of the Fermat numbers and their factors of the form
Michal Křížek, Jan Chleboun (1994)
Mathematica Bohemica
Similarity:
We show that any factorization of any composite Fermat number into two nontrivial factors can be expressed in the form for some odd and , and integer . We prove that the greatest common divisor of and is 1, , and either or , i.e., for an integer . Factorizations of into more than two factors are investigated as well. In particular, we prove that if then and .