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

I made an unwarranted assumption that the integers in 25! had to be used without factoring them. The problem, as stated, does not require this. Therefore, 25! can be factored  uniquely into the first 9 primes and powers of those primes. These 9 relatively prime integers can be separated into two parts (m,n) 512 different ways. Half of them will be in (0,1) and half will not. The answer is back to 256. Sorry about the detour.
    Fogey

Posted by Larry Settle on 2006-10-07 15:25:46