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It contradicts minimality because the remainder can be expressed as a linear combination of a and b. If the remainder is positive and smaller than d, it belongs to the set of positive linear combinations, violating the definition of d as the smallest such value.

Conditions: d is defined as the least positive integer linear combination of a and b.; The remainder r is obtained by dividing a or b by d.; r is positive and $r < d$.

It contradicts minimality because the remainder can be expressed as a linear combination of a and b. If the remainder is positive and smaller than d, it belongs to the set of positive linear combinations, violating the definition of d as the smallest such value.

Conditions: d is defined as the least positive integer linear combination of a and b.; The remainder r is obtained by dividing a or b by d.; r is positive and $r < d$.