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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.

Submitted by K Sengupta

Rating: 4.0000 (3 votes)

Solution: (Hide)

P=1 Q=2 R=4 S=8 T=16 and the maximal value is (1/2 + 1/4 + 1/8 + 1/16)=15/16=0.9375
For an explanation, refer to the solution submitted by Gamer in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
re: Extension (and ideas)	Steve Herman	2008-10-05 11:05:39
Extension (and ideas)	Gamer	2008-10-04 13:51:26
re(2): a stab (proof)	Steve Herman	2008-10-04 01:06:44
Solution	Dej Mar	2008-10-03 21:22:54
re: a stab (proof)	Daniel	2008-10-03 14:24:29
a stab	Leming	2008-10-03 14:12:20
looks obvious .......spoiler	Ady TZIDON	2008-10-03 12:36:47

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