Corpus v3 · Formal theorem
cid005335
FTH0073canonicalv1no_elliptic_idempotent (theorem)
/-- [I.T10] No nontrivial idempotent in the Gaussian integers: if (a+bi)² = (a+bi) over Z, then (a,b) = (0,0) or (a,b) = (1,0). Proof: From (a+bi)² = a+bi: - Real part: a² - b² = a - Imaginary part: 2ab = b From 2ab = b: either b = 0 or 2a = 1 (impossible in Z). If b = 0: a² = a, so a(a-1) = 0, hence a = 0 or a = 1. -/
Formalization
lean_axiom_freesorries: 0project axioms: 0
Identifiers
Aliases & legacy IDs
no_elliptic_idempotentno-elliptic-idempotentTauLib.BookI.Polarity.BipolarAlgebra::no_elliptic_idempotentRelease lines
corpus_v2corpus_v3_workingVersion & History
Status disclaimer
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