Product of 3 Consecutive Integers is Divisible by 6
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Theorem
Let $a, b, c \in \Z$ be consecutive integers.
Then their product $a b c$ is divisible by $6$.
Proof
This is an application of Divisibility of Product of Consecutive Integers with $n = 3$.
By the theorem, the product of $3$ consecutive integers is divisible by $3! = 6$.
$\blacksquare$
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 $2.2$: $14$