take $a= -2022, d=2022, b=c=0$, so the answer is $d=2022$, something feels wrong

@above -2022 and 0 are not relatively prime.

$b|ac\Rightarrow b|c$,ket $c=bk$,then $d=-ak$ so $a+b+bk-ak=0,(a-b)|(a+b)$ which means $|a-b|=1$ or $2$ (1)$|a-b|=1$,then $|k|=|a+b|,|d|=|a(a+b)|$,its maximum value is $32\cdot (32+31)=2016$ (2)$|a-b|=2,2\nmid a,b$,then $|k|=|\frac{a+b}{2}|,|d|=|a\frac{a+b}{2}|$ its maximum value is $45\cdot 44=1980$ so the maximum is $2016$