TITLE: How to prove $641|2^{32}+1$
QUESTION [6 upvotes]: Possible Duplicate:
To show that Fermat number $F_{5}$ is divisible by $641$. 

How to prove that $641$ divides $2^{32}+1$? What the technical way will be for this question? I want to teach it to my students. Any help. :-)

REPLY [7 votes]: In light of Peter's comment:
we have:
$2^2=4$,
$2^4=16, 2^8=256,$
$2^{16}=256^2=65536=641k_1+154,$   
$2^{32}=641k_2+154^2=641k_3+640$
the rest is very easy.