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same_parity_betrothed

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**Same parity betrothed numbers conjecture.** Do there exist betrothed numbers $(m, n)$ where both have the same parity (both even or both odd)? All known betrothed pairs consist of one even and one odd number.

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Lean 4 Statement 
theorem same_parity_betrothed :
    answer(sorry) ↔ ∃ m n : ℕ, IsBetrothed m n ∧ (Even m ↔ Even n)
ID: Wikipedia__BetrothedNumbers__same_parity_betrothed
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