First Question: Let Nn be the integer whose decimal expansion consists of n consecutive ones. For example, N2=11 and N7=1,111,111. Show that Nn|Nm iff n|m. Second Question: If (a,c)=1, prove that (a,bc)=(a,b). On the second question I can see that it is true because a and c are relatively prime, I realize that ax1+bx2=1, but I'm having difficulty expressing it in a proof satisfactory way. I think I'm just over looking a fact somewhere in my text. As for the first one, I'm not very certain as to where at all to start, so any and all help here would be appreciated. Note that I'm not really wanting the full proof of either, more or less just a few helpful pointers or some key facts that are needed that I'm missing; something to get me started so I can get a better attempt at it. If anything is unclear, I'll be happy to restate it in a more satisfactory format if possible. Thanks all. Thanks all.