The correct answer to this open question is the following.
The problem that the United States and Russia still have to solve after the cold war is to prevent nuclear war by reducing nuclear weapons.
This issue continued after the Cold War years in which both countries were engaged in an arms race to produce nuclear weapons. In those years, the Soviet Union and the US signed the SALT Treaty 1 and years later the SALT treaty 2. SALT stands for Strategic Arms Limitation Talks. But today, arms control and arms reduction are still being a major issue for both countries.