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 Sum Inverse LCMs (Posted on 2008-10-03)
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

Note: [x, y] represents the LCM of x and y.

 No Solution Yet Submitted by K Sengupta Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Extension (and ideas) Comment 7 of 7 |
(In reply to Extension (and ideas) by Gamer)

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.
 Posted by Steve Herman on 2008-10-05 11:05:39

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