## Gaps in sequantial list.

If I have a sequence 1,2,3,.. 1000. I can find a gap by summing up and subtrating from the sum of 1.. 1000 (usually with a known formula like n x (n+1) / 2 but with processing power I can just add 1 ... 1000 with a computer program).
If there is a two number gap, I can add squares as well and so have two equations with two variables
SumOfOneTo1000 - SumOfListWithGaps = x + y --- Equation 1
SumOfOneSquareTo1000Sequare - SumOfSquaresFromListWithGaps = sqr(x) + sqr(y) ---- Eq 2
Now I have two equations and two unknown and I can simplify that into a quadratic equation with two roots. The roots are x and y.
So I can a 2 number gap as well.
How far can I go with this logic meaning with cubes and 3 gaps etc.
What category does this problem fall under, is it information theory?

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 Blog Entries: 2 You are correct, that you can form n equations of n unknowns of the form: $$A_(1)^(i) + A_(2)^(i) + ... A_(n)^(i) = X_(i)$$ i = {1,2,...,n}. But equations with i > 3 would fall in the category of higher algebra and would be difficult to solve.

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