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SMO 2013 Open Round 1 Question 24

SMO · SMO 2013 Open Round 1

Question 24

Let $a,b,c,d$ be $4$ distinct nonzero integers such that $a+b+c+d=0$ and the number $M=(bc-ad)(ac-bd)(ab-cd)$ lies strictly between $96100$ and $98000$. Determine the value of $M$.