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1. (a) For each of x = 1, 2, 3, 4, 5, 6 find a ∈...

1. (a) For each of x = 1, 2, 3, 4, 5, 6 find a ∈ {0, 1, ..., 6} where x 2 ≡ a (mod 7).

(b) Does x 2 ≡ a (mod 7) have a solution for x every integer a? Justify your answer!

(c) For a ∈ {1, ..., 6} (so a not equal to 0!), how many solutions for x are there in the equation x 2 ≡ a (mod 7)?

What is the pattern here?

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