perplexus.info :: Sequences : Geometric, Arithmetic and Harmonic Harness

Geometric, Arithmetic and Harmonic Harness (Posted on 2014-10-19)

Each of A, B, C and D is a positive integer with A < B < C < D
having gcd(A, B, C, D) = 1 such that:

(i) A, B and C are in geometric sequence, and:
(ii) B, C and D are in arithmetic sequence, and:
(iii) A, B and D are in harmonic sequence.

Does there exist an infinite number of quadruplets satisfying the given conditions? Give reasons for your answer.

Submitted by K Sengupta

Rating: 4.0000 (2 votes)

Solution: (Hide)

(4,6,9,12) is the only quadruplet that satisfy the given conditions.
There DOES NOT exist an infinite number of quadruplets that satisfy the given conditions.
For an explanation, refer to the solution submitted by Steve Herman here and here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re(2): Analytical solution .. I beg to differ)	Steve Herman	2014-10-19 12:24:08
re: Analytical solution .. I beg to differ)	Ady TZIDON	2014-10-19 10:56:36
Analytical solution (spoiler)	Steve Herman	2014-10-19 09:36:51

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