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  • Mathlib/NumberTheory/LegendreSymbol/QuadraticChar

Mathlib/NumberTheory/LegendreSymbol/QuadraticChar/Basic.lean

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@@ -160,7 +160,7 @@ theorem quadraticChar_eq_neg_one_iff_not_one {a : F} (ha : a ≠ 0) :
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/-- For `a : F`, `quadraticChar F a = -1 ↔ ¬ IsSquare a`. -/
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theorem quadraticChar_neg_one_iff_not_isSquare {a : F} : quadraticChar F a = -1 ↔ ¬IsSquare a := by
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by_cases ha : a = 0
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· simp only [ha, MulChar.map_zero, zero_eq_neg, one_ne_zero, isSquare_zero, not_true]
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· simp only [ha, MulChar.map_zero, zero_eq_neg, one_ne_zero, IsSquare.zero, not_true]
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· rw [quadraticChar_eq_neg_one_iff_not_one ha, quadraticChar_one_iff_isSquare ha]
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/-- If `F` has odd characteristic, then `quadraticChar F` takes the value `-1`. -/

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