Can you please show me step by step for this math that makes me undertandable. Q: Determine which of the following congruences have solutions, and find any solutions (between 0 and the modulus) by trial and error. (a) 4x ≡ 5 (mod 6). (b) 6x ≡ 3 (mod 9). (c) x 2 ≡ 2 (mod 4)

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Can you please show me step by step for this math that makes me undertandable.

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

(a) 4x ≡ 5 (mod 6).

(b) 6x ≡ 3 (mod 9).

(c) x 2 ≡ 2 (mod 4)

 

Solution : For all of these, just plug in all integers between 0 and the modulus to see which, if any, work. (a) No solutions. (b) x 2, x 5, x 8. (c) No solutions.For all of these, just plug in all integers between 0 and the modulus to see which, if any, work. (a) No solutions. (b) x 2, x 5, x 8. (c) No solutions.

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