Mathematics, 13.03.2020 05:26 quanharris2k19
6. Prove that the diophantine equation 3x 2 + 4y 2 = 5z 2 has no non-trivial (i. e. (x, y, z) (0,0,0)) solutions. [Give a proof by contradiction. Obtain a contradiction by proving that if there is a non-trivial solution then there is a solution (x1 , y1 , z1 ) with x1 0 mod 5 or y1 0 mod 5.] Deduce that the equation 3x 2 + 4y 2 = 5 has no rational solutions.
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6. Prove that the diophantine equation 3x 2 + 4y 2 = 5z 2 has no non-trivial (i. e. (x, y, z) (0,0,0...
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