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 Sequence Group III (Posted on 2008-10-28)
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 No Rating 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 formula Dej Mar 2008-10-30 00:56:14 proof--thanks to Dej Mar's formula Charlie 2008-10-29 11:58:22 re: computer solutions -- no proof Dej Mar 2008-10-29 10:09:47 computer solutions -- no proof Charlie 2008-10-28 18:58:53 a start Dej Mar 2008-10-28 10:38:15

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