Let $\mathbb{N}$ denote the set of positive integers.

We define a relation $R\subseteq \mathbb{N}^3$ by

$$ R = \{(x,y,z) \in \mathbb{N}^3: \exists n\in \mathbb{N}: 1< n \leq \max\{x,y,z\} \land \exists k\in \mathbb{N}: x^k + y^k \equiv z^k (\text{mod } n)\}.$$

What is an example of an element of $\mathbb{N}^3\setminus R$?