In mathematics, a divisibility sequence is an integer sequence
indexed by positive integers n such that for all m, n. That is, whenever one index is a multiple of another one, then the corresponding term also is a multiple of the other term.
The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined.
A strong divisibility sequence is an integer sequence
such that for all positive integers m, n, Every strong divisibility sequence is a divisibility sequence:
gcd ( m , n ) = m
Therefore, by the strong divisibility property,
gcd (