Find two no. between 60 and 70 that divides
$$\large 2^{43}-1$$

Question

Find two no. between 60 and 70 that divides 
$$\large 2^{43}-1$$

anonymous · Answer

@mukushla

anonymous · Answer

You must first read "The little Fermat theorem" it is very elementary (residues) and plenty of examples identical to your question are given. May be even whole lessons are there

anonymous · Answer

Hey @shubham.bagrecha  do u read my suggestion ?

parthkohli · Answer

It's Fermat's Little Theorem.

anonymous · Answer

looking about it

parthkohli · Answer

$$a^{n - 1} -1 $$is divisible by $n$ if $a$ is an integer.

anonymous · Answer

DON'T forget to medal... later

anonymous · Answer

first ans. the ques.  i've posted.

anonymous · Answer

I prefer to give you the fishing gera and not the fish...

parthkohli · Answer

So, basically, $a = 2$... but we don't have to look at that.
Let's look at 43.
$43 = n - 1 \implies n = 44$

parthkohli · Answer

One number is 44. Got it?

zzr0ck3r · Answer

that dude loves to tell people to medal, very cute. I wish I could give him 20

parthkohli · Answer

But we have to find between 60 and 70 :/

anonymous · Answer

then?

parthkohli · Answer

Let me write a little program.

anonymous · Answer

@zzr0ck3r  what is worse 
A) To help and expect what is commonly considered due in this place (read the rules)
B) To get help and not give thanks ? (you can read the statistics - people do it all the time here !)

anonymous · Answer

and parth n is prime

parthkohli · Answer

Oh wait... yes!

zzr0ck3r · Answer

I said I thought it was cute....

anonymous · Answer

that is an odd number so u must check 61,63,65,67,69

parthkohli · Answer

Doesn't work for any...

anonymous · Answer

yup

anonymous · Answer

shubham can u find the remainder when we divide it by 3

anonymous · Answer

Oh so generous - the first guy who indicated the method - got what he deserved. Should have known by the nick WHO is the asker.....

zzr0ck3r · Answer

@Mikael I dont give help to get thanks, this is not a great way to live my life(for me). The rules say nothing about having to give medals. I guess I only said something because it is sort of like asking for a tip; I have worked in the service industry and would never dare to ask for a tip. If one has to ask for "thanks", the the thanks has no meaning in and of itself. imho. this may be the wrong place for this...

anonymous · Answer

divide what ?

anonymous · Answer

when we divide $$\large 2^{43}-1$$by 3

anonymous · Answer

@zzr0ck3r  I kind of guessed the nature of the person asking here - despite the FIRST DIRECTION - no thx.

anonymous · Answer

how will we divide?

anonymous · Answer

what methods do u know for such problems?

anonymous · Answer

no method

anonymous · Answer

pls tell me some methods

anonymous · Answer

sorry its not easy to explain modular arethmetic fundamentals here !! at least for me