(1) when q=2 and n=3, m = {0, 1}, a = {x | x = x 1+x2? 2+x3? 2 2,xi∈M,I = 1,2,3}。 Set a can be obtained.
(2) Because ai, bi∈M, i= 1, 2, …, N. An < BN, an-BN ≤- 1. S-T =(a 1-b 1)+ can be obtained from the meaning of the question. 1? bn? 1)q^(n? 2)+ (Ann? bn)q^(n? 1) ≤-[1+q+…+q (n-2)+q (n-1)], and then we can get it by using the first n terms and formulas of geometric series.
Answer:
(1) solution: when q=2 and n=3, m = {0, 1}, a = {x | x = x 1+x2? 2+x3? 2 2,xi∈M,i= 1,2,3}。 We can get A={0, 1, 2, 3, 4, 5, 6, 7}.
(2) proof: let s, t∈A, s = a1+a2q+…+Anq (n-1), t = b1+b2q+…+bnq (n-/kloc-0 bn? 1)q^(n-2)+(an? bn)q^(n- 1)≤-[ 1+q+…+q^(n-2)+q^(n- 1)]=? [q^(n]? 1/q? 1]