Consider sequences a0,a1,a2,⋯ of non-negative integers defined by selecting any a0,a1,a2 (not all 0) and for each n ≥ 3 letting
an = |an−1 - an−3|1-In the particular case that a0 = 1,a1 = 3 and a2 = 2, calculate the beginning of the sequence, listing
a0,a1,⋯,a19,a20.2-Prove that for each sequence, there is a constant c such that ai ≤ c for all i ≥ 0. Note that the constant c my depend on the numbers a0,a1 and a23-Prove that, for each choice of a0,a1 and a2, the resulting sequence is eventually periodic.4-Prove that, the minimum length p of the period described in (3) is the same for all permitted starting values
a0,a1,a2 of the sequence GMO-Gulf Mathmatical Olympiadalgebra