I need to use the following theorem in a paper but have to expect that some of the audience (physicists) is not familiar with it, so I would like to reference it:
Let $a$ and $b$ be two coprime integers. Let $f(k) := ka \bmod b$. Then $$k≠j ⇒ f(k) ≠ f(j) \quad ∀ k,j ∈ \left\lbrace 0, …, b-1 \right\rbrace$$ or with other words: $f$ is a bijection on $\left\lbrace 0, …, b-1 \right\rbrace$.
What is the name of this theorem and if it does not have one, what is a sligthly more general theorem to reference instead? If even this does not exist, I am interested in a citable reference for this.
I have gone through Wikipedia’s lists of theorems and lemmas and checked everything named by less than two persons and did not find anything. I also checked a few books on number theory and did not find this statement.
Note that I am not looking for a proof (I can do that myself).