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Johndcook
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135
Millionth powers
- Find a positive integer n < 10,000,000 such that the first four digits (in the decimal expansion) of n1,000,000 are all different.
- The solution is not unique, but the solution Stanley gives is n = 1,000,001.
- Let M = 1,000,000. We will show that the first four digits of (M + 1)M are 2718.
- There are many other solutions: 7, 8, 12, 14, 16, ...
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