The well-ordering principle guarantees this by ensuring that any nonempty set of positive integers has a smallest element. Since the set of positive linear combinations is nonempty, it must contain a minimum value.
Conditions: Integers a and b are not both zero.; The set consists of positive values of the form au+bv where u and v are integers.
The well-ordering principle guarantees this by ensuring that any nonempty set of positive integers has a smallest element. Since the set of positive linear combinations is nonempty, it must contain a minimum value.
Conditions: Integers a and b are not both zero.; The set consists of positive values of the form au+bv where u and v are integers.