Euler problems/61 to 70

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Problem 61

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


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Problem 62

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


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Problem 63

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


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Problem 64

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


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Problem 65

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


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Problem 66

Investigate the Diophantine equation x2 − Dy2 = 1.


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Problem 67

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


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Problem 68

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


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Problem 69

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


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Problem 70

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


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