# Euler problems/61 to 70

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BrettGiles (Talk | contribs) m (EulerProblems/61 to 70 moved to Euler problems/61 to 70) |
(→[http://projecteuler.net/index.php?section=problems&id=66 Problem 66]: eqn fix) |
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== [http://projecteuler.net/index.php?section=problems&id=66 Problem 66] == | == [http://projecteuler.net/index.php?section=problems&id=66 Problem 66] == | ||

− | Investigate the Diophantine equation | + | Investigate the Diophantine equation x<sup>2</sup> − Dy<sup>2</sup> = 1. |

Solution: | Solution: |

## Revision as of 03:20, 29 March 2007

## Contents |

## 1 Problem 61

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

Solution:

problem_61 = undefined

## 2 Problem 62

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

Solution:

problem_62 = undefined

## 3 Problem 63

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

Solution:

problem_63 = undefined

## 4 Problem 64

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

Solution:

problem_64 = undefined

## 5 Problem 65

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

Solution:

problem_65 = undefined

## 6 Problem 66

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

Solution:

problem_66 = undefined

## 7 Problem 67

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

Solution:

problem_67 = undefined

## 8 Problem 68

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

Solution:

problem_68 = undefined

## 9 Problem 69

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

Solution:

problem_69 = undefined

## 10 Problem 70

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

Solution:

problem_70 = undefined