Consider the value of n(n² - 1)(n² - 4) for each integer n ≥ 3. What is the greatest positive integer that divides this value for every such n?

MathematicsHardHigh School (11–12)Number Systems › Divisibility, HCF and LCM Olympiad

Consider the value of $n(n^2 - 1)(n^2 - 4)$ for each integer $n \ge 3$ . What is the greatest positive integer that divides this value for every such $n$ ?

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