Question 108
Four distinct integers are written on the board. It is known that the absolute value of each of them is greater than $10^6$, and there is no positive integer greater than $1$ which divides all these numbers. Pete wrote on a paper six pairwise sums of the numbers from the board. Then he partitioned the obtained six numbers into three pairs and multiplied the numbers in each pair. May it happen that all three obtained products are equal?