Start with a vector (ordered quadruplet) of any four integers. Construct a new such vector that is the difference between successive elements of the first, cyclically so that the last difference is that between the last element of the first sequence and the first element of that array. Always take the absolute value when doing the differences. Call this the "diffy" operation.

If we repeat the diffy operation starting with the sequence (3, 7, 1022, 2005) we get the following.

(3, 7, 1022, 2005)

(4, 1015, 983, 2002)

(1011, 32, 1019, 1998)

(979, 987, 979, 987)

(8, 8, 8, 8)

(0, 0, 0, 0)

True or False: Any starting sequence of integers leads to the zero vector in finitely many steps. Offer proof.