---
id: 5900f4861000cf542c50ff98
title: 'Problem 281: Pizza Toppings'
challengeType: 5
forumTopicId: 301932
dashedName: problem-281-pizza-toppings
---

# --description--

You are given a pizza (perfect circle) that has been cut into $m·n$ equal pieces and you want to have exactly one topping on each slice.

Let $f(m,n)$ denote the number of ways you can have toppings on the pizza with $m$ different toppings ($m ≥ 2$), using each topping on exactly $n$ slices ($n ≥ 1$). Reflections are considered distinct, rotations are not.

Thus, for instance, $f(2,1) = 1$, $f(2,2) = f(3,1) = 2$ and $f(3,2) = 16$. $f(3,2)$ is shown below:

<img class="img-responsive center-block" alt="animation with 16 ways to have 3 different toppings on 2 slices each" src="https://cdn.freecodecamp.org/curriculum/project-euler/pizza-toppings.gif" style="background-color: white; padding: 10px;">

Find the sum of all $f(m,n)$ such that $f(m,n) ≤ {10}^{15}$.

# --hints--

`pizzaToppings()` should return `1485776387445623`.

```js
assert.strictEqual(pizzaToppings(), 1485776387445623);
```

# --seed--

## --seed-contents--

```js
function pizzaToppings() {

  return true;
}

pizzaToppings();
```

# --solutions--

```js
// solution required
```