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

The rest(call it  R) are all the factors that must be lumped together to satisfy the condition of relatively prime. They are: All the even numbers, three and all its multiples (since 3 divides 6), five and all its multiples (since 5 divides 10), seven and its multiples (since 7 divides 14), 11 and its mutiple (since 11 divides 22). Thus the only factors of 25! that can be used to form m/n and satisfy the relatively prime condition are 23,19,17,13, and R. To see that this is true, try to move any factor in R from n to m.
    Fogey

Posted by Larry Settle on 2006-10-06 22:45:03