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Problem #342

Fraction decomposition
 Public ★(x7) 08/05/16 by Philippe_57721 8xp Programming 25.9%

There is a smallest $n$ for which there exists a set of distinct integers $S = \{ s_1, s_2, \dots, s_n \}$ such as
$\frac{17}{670} = (1-\frac{1}{s_1})\times(1-\frac{1}{s_2})\times\dots\times(1-\frac{1}{s_n})$

Actually, for this least n the set S is unique.

You are given that S is composed of the union of no more than 4 subsets of consecutive integers.

Find S

Answer format: 'the smallest element'-'the largest element' comma separated for each subset.

For instance, if $S = \{2, 3, 4, 5, 11, 12, 13\} = \{2, 3, 4, 5\} \cup \{11, 12, 13\}$, the answer would be: 2-5,11-13

[My timing: 2 sec ]

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