Each of P, Q, R, S and T
are positive integers
with P < Q < R < S < T
. Determine the maximum value
of the following expression.
[P, Q] -1 + [Q, R] -1 + [R, S] -1 + [S, T] -1
: [x, y] represents the LCM
of x and y.
(In reply to Extension (and ideas)
I agree completely with Gamer's points:
a) a series of any length would be more interesting
b) switching any term of 1,2,4,8,16 ... to a larger number results in a smaller result, and doesn't work.
c) We still need to prove that switching a term of 1,2,4,8,16 ... to a small number also results in a smaller result. This hasn't been done yet.