MathDB

Let

A_1 = (0, 0)

B_1 = (1, 0)

C_1 = (1, 1)

D_1 = (0, 1)

. For all

i > 1

, we recursively define

A_i =\frac{1}{2020} (A_{i-1} + 2019B_{i-1}),B_i =\frac{1}{2020} (B_{i-1} + 2019C_{i-1})

C_i =\frac{1}{2020} (C_{i-1} + 2019D_{i-1}), D_i =\frac{1}{2020} (D_{i-1} + 2019A_{i-1})

where all operations are done coordinate-wise. https://cdn.artofproblemsolving.com/attachments/8/7/9b6161656ed2bc70510286dc8cb75cc5bde6c8.png If

[A_iB_iC_iD_i]

denotes the area of

A_iB_iC_iD_i

, there are positive integers

a, b

, and

c

such that

\sum_{i=1}^{\infty}[A_iB_iC_iD_i] = \frac{a^2b}{c}

, where

b

is square-free and

c

is as small as possible. Compute the value of

a + b + c

Problem Statement