Learn Prove halving and subtraction rules, preserve integer Bezout coefficients, and distinguish a plausible answer from an independently checkable gcd certificate.
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Coefficient tracking and gcd preservation are separate obligations.
No. The positive proposed gcd must also divide both inputs. Together, common divisibility and an integer linear-combination identity certify the greatest common divisor.
Swapping values preserves their gcd but can repeat forever.
No. Supply a strictly decreasing nonnegative integer potential or another well-founded argument, and check the terminal condition separately.
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Repair the trace and certify the result
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Replace division by guarded halving and subtraction, tracking an external power of two and a decreasing integer potential.
6 practice tasks.
Normalize a common power of two, repair odd coefficient rows before halving, and verify the final gcd with an independent arithmetic certificate.
6 practice tasks.