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By the definition of division with remainder, for any integers $a$ and $b$ ($b>0$), there exist unique integers $q$ and $r$ such that $a = bq + r$ and $0 \le r < b$. This constraint on $r$ ensures that the remainder is always strictly smaller than the divisor $b$, which is crucial for the algorithm's termination.

Conditions: $b$ is a positive integer.; $a$ is a nonnegative integer.; The operation is $a \bmod b$.

By the definition of division with remainder, for any integers $a$ and $b$ ($b>0$), there exist unique integers $q$ and $r$ such that $a = bq + r$ and $0 \le r < b$. This constraint on $r$ ensures that the remainder is always strictly smaller than the divisor $b$, which is crucial for the algorithm's termination.

Conditions: $b$ is a positive integer.; $a$ is a nonnegative integer.; The operation is $a \bmod b$.