62nd Ukrainian National Mathematical Olympiad, Third Round, First Tour

If some two products are equal, then all products are equal, and all numbers are equal. If some two numbers are equal, then some products are equal, so all numbers are equal. Now consider 4 largest numbers $a<b<c<d$. The largest two products are $cd,bd$. Then the difference of the progression is $cd-bd$. But then $ac-ab=a(c-b)<d(c-b)$, so the difference between some two elements of the progression is smaller than the difference of the progression, which is impossible, a contradiction.