Suppose I have a simple polynomial in $ {a, b } $, defined as $ a ^ k-b ^ k forall k in mathbb {Z} ^ { geq0} $. If I know that one of the factors is $ (a-b) $is there a way to get a representation of its remaining factors in Wolfram Language?

I know that one of his representations is $ sum_ {j = 0} ^ {k-1} {(a ^ {(k-1) -j} b ^ j)} $ and Mathematica recognizes that

```
Sum[a^((k-1)-j) b^j,{j,0,k-1}]
```

given

```
(a ^ k - b ^ k) / (a - b)
```

But if I ask

```
FullSimplify[(a^k-b^k)/(a-b),Assumptions->k[Element]NonNegativeIntegers]
```

He is unable to do anything.

Also, what is the right way to formulate hypotheses?

Is the expression above interpreted differently if I give as

```
Supposing[k[Element]NonNegativeIntegers, FullSimplify[(a^k-b^k)/(a-b)]]
```

Also tried to factoring directly without giving a single factor without success,

```
Supposing[k[Element]NonNegativeIntegers, Factor[a^k-b^k]]
```