freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-374-maximum-integer-partition-product.english.md

---
id: 5900f4e51000cf542c50fff6
challengeType: 5
title: 'Problem 374: Maximum Integer Partition Product'
---

## Description
<section id='description'>
An integer partition of a number n is a way of writing n as a sum of positive integers.

Partitions that differ only in the order of their summands are considered the same.
A partition of n into distinct parts is a partition of n in which every part occurs at most once.

The partitions of 5 into distinct parts are:
5, 4+1 and 3+2.

Let f(n) be the maximum product of the parts of any such partition of n into distinct parts and let m(n) be the number of elements of any such partition of n with that product.

So f(5)=6 and m(5)=2.

For n=10 the partition with the largest product is 10=2+3+5, which gives f(10)=30 and m(10)=3.
And their product, f(10)·m(10) = 30·3 = 90

It can be verified that
∑f(n)·m(n) for 1 ≤ n ≤ 100 = 1683550844462.

Find ∑f(n)·m(n) for 1 ≤ n ≤ 1014.
Give your answer modulo 982451653, the 50 millionth prime.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler374()</code> should return 334420941.
    testString: assert.strictEqual(euler374(), 334420941, '<code>euler374()</code> should return 334420941.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler374() {
  // Good luck!
  return true;
}

euler374();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>