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

25! separates into 9 integers by means of a prime sieve. Combinations of these integers are the only ones that satisfy the initial constraint of relatively prime. The number of unique pairs is 1+9+36+84+126=256. Each pair can only be arranged one way to satisfy (0,1).
        fogey

Posted by Larry Settle on 2006-10-04 16:21:12