Difference between revisions of "Euler problems/61 to 70"
BrettGiles (talk | contribs) m (EulerProblems/61 to 70 moved to Euler problems/61 to 70) |
|||
Line 40: | Line 40: | ||
== [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
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 x2 − Dy2 = 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