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

## n and n-1

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- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

### n and n-1

"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

### Re: n and n-1

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.

- cmacis
**Posts:**754**Joined:**Wed Dec 13, 2006 5:22 pm UTC**Location:**Leeds or Bradford, Thessex-
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Is this a problem stated to be solved, or random ponderings?

I like this one anyway. I'll pass the word around a bit.

I like this one anyway. I'll pass the word around a bit.

li te'o te'a vei pai pi'i ka'o ve'o su'i pa du li no

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

Mathematician is a function mapping tea onto theorems. Sadly this function is irreversible.

QED is Latin for small empty box.

Ceci nâ€™est pas une [s]pipe[/s] signature.

- 3.14159265...
- Irrational (?)
**Posts:**2413**Joined:**Thu Jan 18, 2007 12:05 am UTC**Location:**Ajax, Canada

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.

"The best times in life are the ones when you can genuinely add a "Bwa" to your "ha""- Chris Hastings

### Re: n and n-1

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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