# Homework Help: Canonical Decomp

1. Jun 18, 2010

### Dustinsfl

$$2^{27}+1=(2^9)^3+1^3=(2^9+1)(2^{18}-2^9+1)=(2^3+1)(2^6-2^3+1)(2^{18}-2^9+1)$$

Now what?

2. Jun 18, 2010

### Dick

That would really depend a lot on what the question is. Wouldn't it?

3. Jun 18, 2010

### Dustinsfl

Canonical Decomp.

4. Jun 18, 2010

### Dick

I give up. What's Canonical Decomp?

5. Jun 18, 2010

### Dustinsfl

Canonical Decomp of a $\mathbb{Z}^+$ $n$ is of the form $n=p_{1}^{a_1}*p_{2}^{a_2}\dots p_{k}^{a_k}$, where $p_1,\ p_2, \dots \ p_k$ are distinct primes with $p_1,< p_2, < \dots \ <p_k$ and each exponent is a $\mathbb{Z}^+$

6. Jun 19, 2010

### Staff: Mentor

23 + 1 can be factored.

7. Jun 19, 2010

### Staff: Mentor

Also, 26 - 23 + 1 and 218 - 29 + 1 are not prime.