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Show that product is divisible by 48

Source: XIII Polish Junior MO 2018 First Round - Problem 3

April 24, 2018
number theoryprime numbersDivisibilityPoland

Problem Statement

Prime numbers a,b,ca, b, c are bigger that 33. Show that (a−b)(b−c)(c−a)(a - b)(b - c)(c - a) is divisible by 4848.
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