Let $A$ be a ring with $0\neq1$ having $2^n-1$ invertible elements and at most $2^n-1$ non-invertible elements. Then $A$ must be a field? How many elements does the ring need to have? Because $2^n-1$ is odd, the characteristic of the ring is $2$. Thank you!
2026-04-08 15:43:10.1775662990
Finite ring having $2^n-1$ invertible elements
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