MathDB

A square is inscribed in an ellipse such that two sides of the square respectively pass through the two foci of the ellipse. The square has a side length of

4

. The square of the length of the minor axis of the ellipse can be written in the form

a + b\sqrt{c}

where

a, b

, and

c

are integers, and

c

is not divisible by the square of any prime. Find the sum

a + b + c

Problem Statement