Problem 3.  We call a positive integer n peculiar if, for any positive divisor d of n , the integer d ( d + 1) divides n ( n + 1). Prove that for any four diff erent peculiar positive integers A , B , C and D , the following holds:

gcd( A, B, C, D ) = 1 .

Here gcd( A, B, C, D ) is the largest positive integer that divides all of A, B, C and D .