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Sequence Group III (Posted on 2008-10-28) Difficulty: 3 of 5
Five positive integers A, B, C, D and E, with A < B < C < D < E, are such that:

(i) A, B and C (in this order) are in arithmetic sequence, and:

(ii) B, C and D (in his order) are in geometric sequence, and:

(iii) C, D and E (in this order) are in harmonic sequence.

Determine the minimum value of (E-A) such that there are precisely two quintuplets (A, B, C, D, E) that satisfy all the given conditions.

Note: Try to solve this problem analytically, although computer program/ spreadsheet solutions are welcome.

  Submitted by K Sengupta    
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Solution: (Hide)
The required minimum value of (E-A) is 64.

For an explanation, refer to the combination of analytical and computer assisted methodologies by Charlie and Dej Mar in the comments.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: proof--thanks to Dej Mar's formulaDej Mar2008-10-30 00:56:14
Solutionproof--thanks to Dej Mar's formulaCharlie2008-10-29 11:58:22
re: computer solutions -- no proofDej Mar2008-10-29 10:09:47
Solutioncomputer solutions -- no proofCharlie2008-10-28 18:58:53
Some Thoughtsa startDej Mar2008-10-28 10:38:15
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