2021 AIME I Problem 15

Let S be the set of positive integers k such that the two parabolasy=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 21. Find the sum of the least element of S and the greatest element of S.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.