I want to do prime factorization of following $a$

```
a=sqrt(2)+6-sqrt(2)
a.factor()
```

But sage says simply

```
6
```

What should I do?

(I originally wanted to factor (((3+sqrt(8))^(1*i) +(3-sqrt(8))^(1*i))/2) for i in [1..40])

1 | initial version |

I want to do prime factorization of following $a$

```
a=sqrt(2)+6-sqrt(2)
a.factor()
```

But sage says simply

```
6
```

What should I do?

(I originally wanted to factor (((3+sqrt(8))^(1*i) +(3-sqrt(8))^(1*i))/2) for i in [1..40])

I want to do prime factorization of following $a$

```
a=sqrt(2)+6-sqrt(2)
a.factor()
```

But sage says simply

```
6
```

What should I do?

(I originally wanted to factor ~~(((3+sqrt(8))^(1~~$((3+\sqrt{8})^i +(3-\sqrt{8})^i)/2$ for i in [1..40])*i) +(3-sqrt(8))^(1*i))/2)

I want to do prime factorization of following $a$

```
a=sqrt(2)+6-sqrt(2)
a.factor()
```

But sage says simply

```
6
```

What should I do?

(I originally wanted to factor ~~$((3+\sqrt{8})^i +(3-\sqrt{8})^i)/2$ ~~$\frac{(3+\sqrt{8})^i +(3-\sqrt{8})^i}{2}$ for i in [1..40])

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