Five positive integers A
, with A
, are such that:
(in this order) are in harmonic sequence
(in this order) are in geometric sequence, and:
(in this order) are in arithmetic sequence.
Determine the minimum value of (E
) such that there are precisely three quintuplets (A
) that satisfy all the given conditions.
If you start by writing everything in terms of A and B you get
C = AB/(2A-B)
D = A^2B/(2A-B)^2
E = AB^2/(2A-B)^2
I played with excel a bit but didn't discover much.
You can also use the last to solve for B, C and D in terms of A and E, but this requires the quadratic formula and leads to:
B = -2A(Eħ
I haven't found C and D yet.
This actually shows some promise since it implies AE is a perfect square among other things.
Posted by Jer
on 2011-04-05 02:00:21