# Euler problems/61 to 70

## Contents

## Problem 61

Find the sum of the only set of six 4-digit figurate numbers with a cyclic property.

Solution:

```
problem_61 = undefined
```

## Problem 62

Find the smallest cube for which exactly five permutations of its digits are cube.

Solution:

```
problem_62 = undefined
```

## Problem 63

How many n-digit positive integers exist which are also an nth power?

Solution:

```
problem_63 = undefined
```

## Problem 64

How many continued fractions for N ≤ 10000 have an odd period?

Solution:

```
problem_64 = undefined
```

## Problem 65

Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.

Solution:

```
problem_65 = undefined
```

## Problem 66

Investigate the Diophantine equation x^{2} − Dy^{2} = 1.

Solution:

```
problem_66 = undefined
```

## Problem 67

Using an efficient algorithm find the maximal sum in the triangle?

Solution:

```
problem_67 = undefined
```

## Problem 68

What is the maximum 16-digit string for a "magic" 5-gon ring?

Solution:

```
problem_68 = undefined
```

## Problem 69

Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.

Solution:

```
problem_69 = undefined
```

## Problem 70

Investigate values of n for which φ(n) is a permutation of n.

Solution:

```
problem_70 = undefined
```