Determine the total number of quadruplets (A,B, C, D) of positive integers with A ≤ B ≤ C ≤ D ≤ 25, such that (A+B)*(C+D) is divisible by |A*D – B*C|, whenever A*D ≠ B*C.

Note: |x| refers to the absolute value of x.

(In reply to re(2): computer solution ... Do me a favor , Charlie by Charlie)

Thinking more about it, I think the term combi(4,2)*combi(25,2)/2 is better taken as two terms: 2*combi(25,2)+combi(25,2), the first recognizing the possibility of two numbers with one or the other being repeated three times and the other only once, while the solitary combination being the equal distribution of two chosen integers.

Posted by Charlie on 2011-02-07 14:15:35