8. Fermat stated the following three results. Use the topograph and quadratic residues as in Theorem...

 

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8. Fermat stated the following three results. Use the topograph and quadratic residues as in Theorem 10.15 to prove them. (a) If p = 1 mod 6 then p is represented by x? + 3y2. (b) If p = 1 or 3 mod 8 then p is represented by x2 + 2y2. (c) If p = +1 mod 8 then p is represented by x2-2y². 8. Fermat stated the following three results. Use the topograph and quadratic residues as in Theorem 10.15 to prove them. (a) If p = 1 mod 6 then p is represented by x? + 3y2. (b) If p = 1 or 3 mod 8 then p is represented by x2 + 2y2. (c) If p = +1 mod 8 then p is represented by x2-2y².

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of Quadratic Reciprocity law We can use the below theorem found in the results and mo... View the full answer