Theorems · Theorem · number theory

MulChar.pow_card_eq_one

∀ {M : Type u_1} [inst : CommMonoid M] {R : Type u_2} [inst_1 : CommMonoidWithZero R] [inst_2 : Fintype Mˣ]
  (χ : MulChar M R), χ ^ Fintype.card Mˣ = 1

If χ is a multiplicative character on a commutative monoid M with finitely many units, then χ ^ #Mˣ = 1.

Defined in

Mathlib.NumberTheory.MulChar.Basic

Cited by

2 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommMonoidCommMonoidWithZeroFintype