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Source: 2021 AIME 1/15

March 11, 2021
AMCAIME2021 AIME I

Problem Statement

Let SS be the set of positive integers kk such that the two parabolasy=x2−k  and  x=2(y−20)2−ky=x^2-k~~\text{and}~~x=2(y-20)^2-kintersect in four distinct points, and these four points lie on a circle with radius at most 2121. Find the sum of the least element of SS and the greatest element of SS.
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