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(a - b)(a - c)(a - d)(b - c)(b - d)(c - d) is multiple of 12

Source: New Zealand NZMOC Camp Selection Problems 2018 p1

September 19, 2021
multipledividesnumber theory

Problem Statement

Suppose that a,b,ca, b, c and dd are four different integers. Explain why (a−b)(a−c)(a−d)(b−c)(b−d)(c−d)(a - b)(a - c)(a - d)(b - c)(b -d)(c - d) must be a multiple of 1212.
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