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State/Nonmultiples of a prime are relatively prime to the prime
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Proposition: (Nonmultiples of a prime are relatively prime to the prime) Suppose that $p$ is a prime number. Suppose that $a$ is an integer. Then the following two statements are equivalent:
- $a$ is relatively prime to $p$, i.e., $GCD(a,p) = 1$
- $a$ is not a multiple of $p$.
Logical Connections
This statement logically relies on the following definitions and statements: Def/Prime number, Def/Greatest common divisor
The following statements and definitions rely on the material of this page: State/Multiplicative inverses exist mod p
To visualize the logical connections between this statements and other items of mathematical knowledge, you can visit the following cluster(s), and click the "Visualize" tab: Clust/Basic number theory
