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Theorems · Theorem · number theory

FiniteField.two_pow_card

∀ {F : Type u_1} [inst : Fintype F] [inst_1 : Field F],
  ringChar F ≠ 2 → 2 ^ (Fintype.card F / 2) = ↑(ZMod.χ₈ ↑(Fintype.card F))

For every finite field F of odd characteristic, we have 2^(#F/2) = χ₈ #F in F.

Defined in
Mathlib.NumberTheory.GaussSum
Cited by
1 results in Mathlib
Foundations
Depth 219 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FintypeField

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