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Geometric, Arithmetic and Harmonic Harness (Posted on 2014-10-19) Difficulty: 3 of 5
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.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re(2): Analytical solution .. I beg to differ) Comment 3 of 3 |
(In reply to re: Analytical solution .. I beg to differ) by Ady TZIDON)

The correct answer to:

 Does there exist an infinite number of quadruplets satisfying the given conditions?

is  N O.

The problem specifies that gcd(A, B, C, D) = 1 

But gcd(4k, 6k, 9k, 12k) = k, which means that k can only equal 1.

Edited on October 19, 2014, 12:27 pm
  Posted by Steve Herman on 2014-10-19 12:24:08

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