Set of number Where any subset has a unique sum?

sequences-and-series

Consider a set of form $\{a,a+C,a+2C,a+3C\}$, each subset does not have a unique sum. Also, any set of the form you want has a subset of this form, if it has more than 3 elements. So, 3 elements is the biggest you can get of your form.


I think you want to talk about the existence of pairs which differ by one. Note that I could write your set as $\{3, 5, 4\}$, in which case the second element listed on the computer screen is not increased by 1.

For a set $S$, for all $x$ belonging to $S$, there exists a $y$ belonging to $S$, such that $(x-y)=c$. The doesn't work, since for $3$ there doesn't exist such a $y$. I guess maybe

"For a set $S$, for all $x$ belonging to $S$, there exists a y belonging to S, such that $|(x-y)|=1$"

I don't understand your problem otherwise.

Related

Hamming distance equals hamming weight under $XOR$ closure
How many group actions are there of $Q_8$ on a 4 element set.
Integral operator and it’s spectrum
For $x+y=n$, if $V'-V=3$ then $\large \frac{n}2$ is prime.
Christoffel Symbols and the change of transformation law.
Is the union of two nowhere dense sets nowhere dense?
Conclude $L_{[a]}$ is not injective if it is not surjective and use this to show the existence of $[b] \in \mathbb{Z_{n}}$ s.t. $[a][b] = [0]$
Prove $a {a+b \choose b}$ divides the lowest common multiple of $b+1, b+2, ..., b+a$
Proofs in Real Analysis are too 'convenient'
Who that Wirtinger's inequality does not hold when $a>\pi$?
Is it acceptable/usual to write multiple conditional probability pipes simultaneously? eg, $\tilde P(L \mid M_2)\equiv P(L \mid M_2\mid M_1)$
Exponentiating expression containing ln(abs(x))