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Consecutive Count (Posted on 2015-04-23) Difficulty: 3 of 5
Three positive integers 2520 < b < c constitute three consecutive terms of a harmonic sequence and, b divides c.

Find the total count of pairs (b,c) for which this is possible.

No Solution Yet Submitted by K Sengupta    
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Solution Analytic solution | Comment 3 of 4 |
Well, I guess I did have time to do this now.

let c = kb, where k is an integer

Then 1/2520 - 1/b = 1/b - 1/kb

Rearranging,

b = 5040 - 2520/k

k can be any integer > 1 that is a factor of 2520.
So how many factors does 2520 have?

2520 = 2^3 * 3^2 * 5 *7,
so number of factors = 4*3*2*2 = 48

Since k must be > 1, answer is 48 - 1 = 47

Edited on April 24, 2015, 9:24 am
  Posted by Steve Herman on 2015-04-24 09:22:47

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