# "Arithmetic?" proof

This is a self-assigned question. Not homework.

I may have the right answer, but would like some reviewing. It came to me while reading on a CS topic, this did not come from a math textbook, otherwise it would be slightly more in context.

I did not use any formula (so 2 would be empty) and 1 and 3 are in a PDF here.

1. Is my work correct?
2. Is there an easier way to prove it?
3. What exactly is this? I called it an "'Arithmetic?' proof", but I don't think that this would be its name.

#### Attachments

• Proof.pdf
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haruspex
Homework Helper
Gold Member
Looks right, and fairly straightforward. I doubt there's an easier way.
$$\text{Given that } S \text{ is an array of } m \text{ small nonnegative integers and } \alpha \text{ is a prime larger than the largest integer in } S$$
$$\sum_{i=0}^{m-1}\left(\alpha^{m-(i+1)}\times S_{1_i} \right) \ne \sum_{i=0}^{m-1}\left(\alpha^{m-(i+1)}\times S_{2_i}\right) \forall S_1 \ne S_2$$