\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The goal of this exercise is to find all integers \(x \in \mathbb{Z}\) that are solutions to:$$(E) : x^2 + x - 2 \equiv 0 \pmod{13}$$
  1. Find a particular solution \(\alpha\) of \((E)\).
  2. Set \(X = x - \alpha\) to find all solutions of \((E)\).

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