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**Proof_of_life** Which of the following equations have a solution?

(a) $\displaystyle x^2 \equiv$ $\displaystyle 17$ ($\displaystyle mod$ $\displaystyle 29$)

(b) $\displaystyle 3x^2 \equiv$ $\displaystyle 12$ ($\displaystyle mod$ $\displaystyle 31$)

(c) $\displaystyle 2x^2 \equiv$ $\displaystyle 27$ ($\displaystyle mod$ $\displaystyle 41$)

(d) $\displaystyle x^2 +5x \equiv$ $\displaystyle 12$ ($\displaystyle mod$ $\displaystyle 31$)

Could anyone show me how to solve these step by step? I can't just submit my answers as 'has a solution', 'has no solution.' Thanks!