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if-a-b-c-d-Z-b-a-c-a-d-a-c-b-d-b-d-c-prove-that-the-expression-is-divide-into-12-




Question Number 150684 by mathdanisur last updated on 14/Aug/21
if  a;b;c;d∈Z  (b-a)(c-a)(d-a)(c-b)(d-b)(d-c)  prove that the expression is divide  into 12
$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d}\in\mathbb{Z} \\ $$$$\left(\mathrm{b}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{a}\right)\left(\mathrm{d}-\mathrm{a}\right)\left(\mathrm{c}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{b}\right)\left(\mathrm{d}-\mathrm{c}\right) \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{expression}\:\mathrm{is}\:\mathrm{divide} \\ $$$$\mathrm{into}\:\mathrm{12} \\ $$

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