Exercise 9.

Determine which of the following congruences have solutions, and find any solutions (between 0 and the modulus) by trial and error.

  1. \(4x \equiv 5 \pmod 7\text{.}\)

  2. \(6x \equiv 4 \pmod 9\text{.}\)

  3. \(x^2 \equiv 2 \pmod 7\text{.}\)

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