# Division Theorem/Also known as

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## Division Theorem: Also known as

The **Division Theorem** is otherwise known as the **Quotient Theorem**, or (more specifically) the **Quotient-Remainder Theorem** (as there are several other "quotient theorems" around).

Some sources call this the **Division Algorithm** but it is preferable not to offer up a possible source of confusion between this and the **Euclidean Algorithm** to which it is closely related.

It is also known by some as **Euclid's Division Lemma**, and by others as the **Euclidean Division Property**.

## Sources

- 1968: Ian D. Macdonald:
*The Theory of Groups*... (previous) ... (next): Appendix: Elementary set and number theory - 1970: B. Hartley and T.O. Hawkes:
*Rings, Modules and Linear Algebra*... (previous) ... (next): $\S 2.3$: Some properties of subrings and ideals - 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**division** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**division**