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It serves as a certificate because if integer coefficients x and y satisfy ax+by=1, then any common divisor of a and b must divide 1. The only positive integer dividing 1 is 1 itself, proving that the greatest common divisor is 1.

Conditions: a and b are integers.; There exist integers x and y such that ax+by=1.

It serves as a certificate because if integer coefficients x and y satisfy ax+by=1, then any common divisor of a and b must divide 1. The only positive integer dividing 1 is 1 itself, proving that the greatest common divisor is 1.

Conditions: a and b are integers.; There exist integers x and y such that ax+by=1.