8.5. An inheritance consists of several diamonds, valued at $1,000,000. It is known that it can be divided into 5 equal parts, or into 8 equal parts. Find the maximum possible value of the smallest diamond.
8.5. First, prove that the value of the smallest diamond cannot exceed $50,000. According to the problem, this inheritance can be divided into 8 equal parts, each worth $125,000. It is easy to see that at least one of these parts consists of no fewer than 2 diamonds. Therefore, if every diamond worth $125,000 is replaced by 2 diamonds each worth half as much, this will not change the minimum value of the diamonds, nor will it affect the possibility of dividing them into 5 equal parts. After such a replacement, each part will contain at least 2 diamonds, thus there will be at least 16 diamonds in total. If these are divided into 5 equal parts (each worth $200,000), one of these parts will consist of no fewer than 4 diamonds, so there must be a diamond whose value does not exceed $50,000.

Second, the value of the smallest diamond can reach $50,000. For example: the inheritance includes 12 diamonds, with 4 diamonds each priced at $50,000, $75,000, and $125,000.