All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 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.

 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: Analytical solution .. I beg to differ) | Comment 2 of 3 |
(In reply to Analytical solution (spoiler) by Steve Herman)

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

 Search: Search body:
Forums (0)