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max ac if (a + b)/(b + c) = (c + d)/(d + a)

Source: New Zealand MO 2021 Round 1 p7

September 20, 2021
algebrainequalitiesmax

Problem Statement

Let a,b,c,da, b, c, d be integers such that a>b>c>d≥−2021a > b > c > d \ge -2021 and a+bb+c=c+dd+a\frac{a + b}{b + c}=\frac{c + d}{d + a} (and b+c≠0≠d+ab + c \ne 0 \ne d + a). What is the maximum possible value of acac?
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