Math Proof Help

**ivinew** · December 10th 2009, 06:43 PM

Hi, this is my first time posting.

The problem was to prove that the only prime of the form (n^5)-1 is 31.

My plan is to first write that there is another prime of that form and then somehow prove that that prime is the same prime in the above problem, 31.

But I'm not sure how to get there, some help please?

**chisigma** · December 10th 2009, 07:21 PM

Is...

$n^{5}-1 = (n-1)\cdot (n^{4}+n^{3}+n^{2} + n +1)$ (1)

... then $n^{5} -1$ is prime only if $n-1=1$ , i.e. $n=2$ . The primes of the type $2^{k} -1$ are known as 'Mersenne primes'...

Merry Christmas from Italy

$\chi$ $\sigma$

**CaptainBlack** · December 10th 2009, 11:04 PM

Originally Posted by ivinew

Hi, this is my first time posting.

The problem was to prove that the only prime of the form (n^5)-1 is 31.

My plan is to first write that there is another prime of that form and then somehow prove that that prime is the same prime in the above problem, 31.

But I'm not sure how to get there, some help please?

$31^5-1=2\times 3 \times 5^2 \times 11 \times 17351$

CB

**Shanks** · December 11th 2009, 01:44 AM

I think, chisigma is quite right!

**ivinew** · December 11th 2009, 05:14 AM

chisigma!!! Thanks sooo muchh!!!

I see it now~

**HallsofIvy** · December 11th 2009, 05:56 AM

Originally Posted by CaptainBlack

$31^5-1=2\times 3 \times 5^2 \times 11 \times 17351$

CB

I don't understand. What does $35^5- 1$ have to do with $n^5- 1= 31$ ?

**CaptainBlack** · December 11th 2009, 07:52 AM

Originally Posted by HallsofIvy

I don't understand. What does $35^5- 1$ have to do with $n^5- 1= 31$ ?

nothing I misread the question

CB

**HallsofIvy** · December 11th 2009, 08:35 AM

You mean I'm not the only one who does that?

**Danny** · December 12th 2009, 09:05 AM

Originally Posted by HallsofIvy

You mean I'm not the only one who does that?

Me too

Thread: Math Proof Help

LinkBack

Thread Tools

Display

Math Proof Help

Similar Math Help Forum Discussions

Math proof regarding gcd

Math proof help

Math Proof

I need help with a math proof

Math proof help

Search Tags