Simple example in order to clarify what I mean:
Sequence - $\{2 , -1, 4, 2, 9 \}$ Sum and product combination: $\{ 16, -144 \}$
Question: Is a combination of sum and product unique for any* sequence?
- "any sequence" except that one which consists only of zeros.
UPD: The answer to my initial question is "no". Thanks. But what's the answer if we restrict ourselves to sequences of the same length and made of non-negative integers? Do two or more non-negative integer sequences exist, each of which has the same {sum,product} combination and the same length?
UPD: Both answers are "no". Thanks a lot.