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What do you call numbers you can add together that will always be unique.

$a = 1,$

$b = 2,$

$c = 4$

Any combination of the above will always result in a unique number. eg:

$7 = abc,$

$6 = bc,$

$3 = ab.$

Sorry if this is a simple maths question, I have tried searching google however I keep coming up short.

Thanks

Kenta S
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Nicholas Mordecai
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  • You mixed the sum and the product , you mean $a+b+c=7$ , $b+c=6$ , $a+b=3$. – Peter Nov 09 '14 at 13:47
  • The numbers $1,2^2,3^3,4^4,...$ also have the desired property. But the powers of $2$ have the additional property that every number is a sum of them containing any element at most once. – Peter Nov 09 '14 at 13:52
  • Related: http://mathoverflow.net/questions/84594/find-the-maximum-set-whose-subset-sum-is-unique-for-every-of-its-subset – Ross Millikan Nov 11 '14 at 05:29

1 Answers1

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Many numbers will show this property

But Let's look at powers of $2$

additive combination of $2^0,2^1,2^2,2^3\cdots$ will give you any positive integer you want

And one number from this set is required to use only once (Notice the binary representation of any Integer)

e.g $23_{10}=10111_{2}$ $$1\times2^4+0\times2^3+1\times2^2+1\times2^1+1\times2^0=2^4+2^2+2^1+2^0=23$$

Aditya Hase
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