Determine the smallest fifth power having the first four digits (reading left to right) as 2,0,2,2.
What is the smallest number having this property?
The fifth root of 2022 is 4.583067..., and of 2023 is 4.583520.... The digit sequence in the fifth root of what is sought must be larger than that of 2022 ans smaller than that of 2023.
If we use just the first four digits, 4583 as the base of the power, that will lead to something beginning 2021..., as the fifth root needs to be somewhat (a small amount) over 4583. But five digits will do: 45831; the 1 is smaller than the 5 that would lead to 2023 and larger lexicographically than 067....
So the answer is 45831^5 = 202207223867161767338151.
The calculations:
>> 2022^(1/5)
ans =
4.58306725321868
>> 2023^(1/5)
ans =
4.58352048377078
>> 45831^5
ans =
2.02207223867162e+23
>> sym(45831)^5
ans =
202207223867161767338151
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Posted by Charlie
on 2023-04-30 09:41:45 |
Solution (spoiler)
