Abstract
AbstractWe investigate a curious problem from additive number theory: Given two positive integers S and Q, does there exist a sequence of positive integers that add up to S and whose squares add up to Q? We show that this problem can be solved in time polynomially bounded in the logarithms of S and Q.As a consequence, also the following question can be answered in polynomial time: For given numbers n and m, do there exist n lines in the Euclidean plane with exactly m points of intersection?
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