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A rational number problem (Posted on 2006-10-02) Difficulty: 3 of 5
Determine the total number of rational numbers of the form m/n, where m and n are positive integers such that:

(A) m/n lies in the interval (0, 1); and

(B) m and n are relatively prime; and

(C) mn = 25!

NOTE: "!" denotes the factorial symbol, where n! = 1*2*3*......*(n-1)*n

See The Solution Submitted by K Sengupta    
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re(2): Got it | Comment 5 of 12 |
(In reply to re: Got it by Dej Mar)

Jer's 2^9/2 already includes the possibility of only 1 as one of the two numbers m or n.

One of the 2's that make up the 2^9 is the decision to include or exclude the 2^22 that goes into the factorization of 25!. Another of the 2's represents the decision to include or exclude the 3^10 that goes into the factorization of 25!. Another represents including or excluding the 5^6, etc.

Note that one of the 2^9 possibilities is to exclude them all from m; that leaves just a factor of 1 to be n. The possibility to include them all in m leaves the other number (n) as 1.  The division by 2 reduces that to just the 1/25! and excudes the 25!/1.

  Posted by Charlie on 2006-10-04 00:08:54
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