gcd(a1, a2, ⋯, an − 2, an − 1, an) = gcd(a1, a2 – a1, ⋯, an – 1 – an − 2, an − an − 1)
gcd(a, b) = gcd(a, b – a)
gcd(a, b, c) = gcd(a, gcd(b, c)) = gcd(gcd(a, b), c)
Then, it can be generalized as:
gcd(a1, a2, ⋯, an−1, an) = gcd(a1, a2, ⋯, an−2, gcd(an−1, an))
= gcd(a1, a2, ⋯, an−2, gcd(an−1, an−an−1))
= gcd(a1, a2, ⋯, an−2, an−1, an−an−1)
= gcd(a1, a2, ⋯, gcd(an−2, an−1), an−an−1)
= gcd(a1, a2, ⋯, gcd(an−2, an−1−an−2), an−an−1)
…
= gcd(a1, a2, ⋯, an−2, an−1−an−2, an−an−1)