1. (15 points) For each of the following statements, indicate whether the statement is true or false and justify your an

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1 15 Points For Each Of The Following Statements Indicate Whether The Statement Is True Or False And Justify Your An 1 (188.6 KiB) Viewed 30 times

1. (15 points) For each of the following statements, indicate whether the statement is true or false and justify your answer with a proof or a counterexample. (a) Let P be an odd prime. If a, ß € Fp are nonsquares, then aß is a square. (b) If m E N with m ≥ 3, then the product of the elements in (Z/mZ)× is congruent to -1 modulo m. (c) The equation X² – 13Y² = 7 has an integral solution, i.e., there is a pair (x, y) = Z² such that x² - 13y² = 7. (d) If p is prime and ß € FX, then the equation Xº – X = ß has no solutions in Fp.