Find all numbers with the property that each is equal to the sum of the cubes of its digits. There aren’t many.
Cinelli
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Cubes
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- The full Lemon
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Re: Cubes
cinelli wrote:Find all numbers with the property that each is equal to the sum of the cubes of its digits. There aren’t many.
Cinelli
There are many. Indeed infinitely many!
Single digits: 1, 0, -1.
From these, 00, 01, 000, 001, 0000, 0001, etc.
But I expect you were looking at cases like
153 = 1 + 125 + 27
370 = 9 + 343 + 0
371 = 9 + 343 + 1
407 = 64 + 0 + 343
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- Lemon Quarter
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Re: Cubes
I found six, and this is all there are.
I have not counted -1 as its digit is 1. If you count negatives, there are five more, e.g., -371 is -3 hundreds, -7 tens and -1 unit.
407 is the same number as 00407.
Julian F. G. W.
I have not counted -1 as its digit is 1. If you count negatives, there are five more, e.g., -371 is -3 hundreds, -7 tens and -1 unit.
407 is the same number as 00407.
Julian F. G. W.
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Re: Cubes
jfgw wrote:I have not counted -1 as its digit is 1. If you count negatives, there are five more, e.g., -371 is -3 hundreds, -7 tens and -1 unit.
Agreed, playing with negatives (or complex numbers) here is a bit dodgy
407 is the same number as 00407.
But the question said nothing about distinct numbers!
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Re: Cubes
UncleEbenezer wrote:But the question said nothing about distinct numbers!
I will let the OP ajudicate.
I would question infinity (expressed as an infinite sequence of digits) too.
Julian F. G. W.
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