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.

(In reply to Analytical solution (spoiler) by Steve Herman)

The correct answer to:

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

is  Y E S.

Their general form is (4k, 6k, 9k, 12k)

Posted by Ady TZIDON on 2014-10-19 10:56:36