Let $a, b, c, d$ be integers such that $a > b > c > d \ge -2021$ and $$\frac{a + b}{b + c}=\frac{c + d}{d + a}$$(and $b + c \ne 0 \ne d + a$). What is the maximum possible value of $ac$?
Source: New Zealand MO 2021 Round 1 p7
Tags: algebra, inequalities, max
Let $a, b, c, d$ be integers such that $a > b > c > d \ge -2021$ and $$\frac{a + b}{b + c}=\frac{c + d}{d + a}$$(and $b + c \ne 0 \ne d + a$). What is the maximum possible value of $ac$?