Prove that 2^n+1 is not divisible by 31

Any ideas on how to start?

Question

Prove that 2^n+1 is not divisible by 31

Any ideas on how to start?

anonymous · Answer

ummmmm...leme think

anonymous · Answer

oh well an odd isnt divisable by an even

whpalmer4 · Answer

$$31=2^5-1$$can you prove anything about what other factors would have to be given that structure?

anonymous · Answer

I'm sorry, I still don't see it. Can you give me another hint or two

whpalmer4 · Answer

I don't have another hint or two, that was just an observation that may or may not prove useful.  It clearly isn't an absolute bar to such a number being a factor, as 9 is divisible by 3...

anonymous · Answer

31 is a prime number!

anonymous · Answer

@whpalmer4 - I've been trying different methods for more than 3 hours now

anonymous · Answer

@clarkydances - yep, that's right. What can we do after that?

anonymous · Answer

...well...u cant multiply anything by any thing to get 31 except 1 and 31

anonymous · Answer

yes. You are correct. But how can we apply that to here?

anonymous · Answer

...yeahhhhh...i got nothing...leme think

anonymous · Answer

okay

anonymous · Answer

do u have to prove with numbers?

anonymous · Answer

no. It should be a general proof

anonymous · Answer

ok...hold on

anonymous · Answer

well i dont know any more proof than 31 is a prime...sorry

anonymous · Answer

It's okay, I appreciate your help

anonymous · Answer

:)

anonymous · Answer

@***[ISURU]*** , dude, any thoughts?