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

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**