Equalities between greatest common divisors involving three coprime pairs

A new equality of the greatest common divisor (gcd) of quantities involving three coprime pairs is proven in this note. For a(i) and b(i) positive integers such that gcd(a(i), b(i)) = 1 for i is an element of {1, 2, 3} and d(ij) = vertical bar a(i)b(j) - a(j)b(i)vertical bar , then gcd(d(32), d(31)) = gcd(d(32), d(21)) = gcd(d(31), d(21)): The proof uses properties of Farey sequences.