Definition:Integer Combination

Definition

Let $a, b \in \Z$.

An integer $n$ of the form:

$n = p a + q b: p, q \in \Z$

is an integer combination of $a$ and $b$.

Also known as

This is also known as:

a linear combination of $a$ and $b$

an integral linear combination of $a$ and $b$.

Also see

• Results about integer combinations can be found here.

Sources

• 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {2-2}$ Divisibility
• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 12$: Highest common factors and Euclid's algorithm
• 1980: David M. Burton: Elementary Number Theory (revised ed.) ... (previous) ... (next): Chapter $2$: Divisibility Theory in the Integers: $2.2$ The Greatest Common Divisor