There are intimate connections between three concepts related to a tuple or list of integers (where at least one of the integers is non-zero): their greatest common divisor or GCD, their collection of common divisors, and their linear combinations. In particular, the smallest positive linear combination is in fact the GCD, the common divisors are the divisors of the GCD, and the linear combinations are the multiples of the GCD. We call this neat classification result Bézout's lemma, with the equation in the first one being called Bézout's identity.
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