Product of 5 Consecutive Integers is Divisible by 120

Theorem

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

Then their product $a b c d e$ is divisible by $120$.

Proof

This theorem requires a proof. In particular: tedious, someone else have a go. Or it's an instance of a general result where the product of $n$ consecutive integers is divisible by $n!$ You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

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 $2.2$: $14$