# Gaps in sequantial list.

by rtal
Tags: gaps, list, sequantial
 P: 2 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? thanks for your help.
 P: 891 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.