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