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2022 IIMC keystage3-IWYMIC individual Question 5

xIMC · 2022 IIMC keystage3-IWYMIC individual

Question 5

Let $a$, $b$, $c$ and $d$ be positive integers such that $0\lt a\lt b\lt c\lt d\lt 2022$, $a+d=b+c$ and $bc-ad=2021$. How many ordered quadruples $(a,b,c,d)$ are there?