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

There are only 5 factors instead of 9.
25!=23x19x17x13x(the rest). With 5 factors that satisfy the relatively prime restriction, there are 1+5+10=16 combinations that form m,n pairs that are relatively prime. There are only 16 rational numbers that are in (0,1).
    Fogey

Posted by Larry Settle on 2006-10-05 17:40:44