n and n-1

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3.14159265...
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n and n-1

Postby 3.14159265... » Fri May 04, 2007 5:44 am UTC

I have come across another problem, while working through my math stuff:

If n=(3^a)(5^b)...(P^c)

Then consider the prime factorization n-1, of course n-1 is even since n was odd so

n-1=(2^d)(3^e)(5^f)...(P^g) with d>0

What is the value of d in terms of a,b.....,c

edit: Also, the full factorization of n-1 would also be nice, but I only need the power of 2 for the problem I am working on now
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notzeb
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Postby notzeb » Fri May 04, 2007 8:23 pm UTC

HAHAHAHAHAHAHAHAHA

OH GOD LOL.

You just made my day.
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Re: n and n-1

Postby Ralp » Fri May 04, 2007 11:58 pm UTC

3.14159265... wrote:n-1=(2^d)(3^e)(5^f)...(P^g) with d>0

What is the value of d in terms of a,b.....,c


I don't know, but it seems like knowing this would solve the 3n-1 problem, which is notoriously unsolved. So, not to be a wet blanket, but I doubt you're going to be able to find a solution. Good luck though.

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Postby cmacis » Sat May 05, 2007 12:01 am UTC

Is this a problem stated to be solved, or random ponderings?

I like this one anyway. I'll pass the word around a bit.
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3.14159265...
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Postby 3.14159265... » Sat May 05, 2007 1:49 am UTC

Ralp wrote:I don't know, but it seems like knowing this would solve the 3n-1 problem, which is notoriously unsolved. So, not to be a wet blanket, but I doubt you're going to be able to find a solution. Good luck though.


Thats exactly where I have encountered it, hm, do you mind sharing how it is that it is THE key for the 3n+1 problem.
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Postby demon » Sat May 05, 2007 9:47 am UTC

Even without involving the 3n+1 problem, when I looked at this I wanted to think up special cases - and a very special case seems to be when n is a Fermat prime. Being able to simply compute such a powerful function would probably be a milestone towards the Fermat prime problem - which is about as notorious as the 3n+1 problem.

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Re: n and n-1

Postby MMoto » Sat May 05, 2007 6:43 pm UTC

3.14159265... wrote:edit: Also, the full factorization of n-1 would also be nice ...


It sure would be nice. That would let you factorise any number n extremely quickly: just choose a prime p bigger than n, then magically compute the full factorisations of p-1, p-2, ..., until you get to n.


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