---
id: 5900f4c71000cf542c50ffd8
title: 'Problem 346: Strong Repunits'
challengeType: 5
forumTopicId: 302005
dashedName: problem-346-strong-repunits
---

# --description--

The number 7 is special, because 7 is 111 written in base 2, and 11 written in base 6 (i.e. $7_{10} = {11}_6 = {111}_2$). In other words, 7 is a repunit in at least two bases $b > 1$.

We shall call a positive integer with this property a strong repunit. It can be verified that there are 8 strong repunits below 50: {1, 7, 13, 15, 21, 31, 40, 43}. Furthermore, the sum of all strong repunits below 1000 equals 15864.

Find the sum of all strong repunits below ${10}^{12}$.

# --hints--

`strongRepunits()` should return `336108797689259260`.

```js
assert.strictEqual(strongRepunits(), 336108797689259260);
```

# --seed--

## --seed-contents--

```js
function strongRepunits() {

  return true;
}

strongRepunits();
```

# --solutions--

```js
// solution required
```