1. ## Math Proof Help

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?

2. Is...

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

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

Merry Christmas from Italy

$\displaystyle \chi$ $\displaystyle \sigma$

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

CB

4. I think, chisigma is quite right!

5. chisigma!!! Thanks sooo muchh!!!

I see it now~

6. Originally Posted by CaptainBlack
$\displaystyle 31^5-1=2\times 3 \times 5^2 \times 11 \times 17351$

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

7. Originally Posted by HallsofIvy
I don't understand. What does $\displaystyle 35^5- 1$ have to do with $\displaystyle n^5- 1= 31$?