Product of 3 Consecutive Integers is Divisible by 6

Theorem

Let $a, b, c \in Z$ be consecutive integers

Then their product $a b c$ is divisible by $6$.

Proof

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Sources

• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor: Problems $2.2$: $14$