Suppose that $a, b, c$ and $d$ are four different integers. Explain why $$(a - b)(a - c)(a - d)(b - c)(b -d)(c - d)$$must be a multiple of $12$.
Problem
Source: New Zealand NZMOC Camp Selection Problems 2018 p1
Tags: multiple, divides, number theory
Source: New Zealand NZMOC Camp Selection Problems 2018 p1
Tags: multiple, divides, number theory
Suppose that $a, b, c$ and $d$ are four different integers. Explain why $$(a - b)(a - c)(a - d)(b - c)(b -d)(c - d)$$must be a multiple of $12$.