For a finite sequence a= (a₁, , a_n ) of n integers (where n 2 ), define S(a)= _ i, j 1,2, , n i j a_i a_j .

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1. AFor a= (a₁, , a_n ) and b= (b₁, , b_m ) , define a b= (a₁, , a_n, b₁, , b_m ) . Then S(a b)=S(a)+S(b) .
2. BIf a is a sequence of m+k integers with m many 1 's and k many -1 's then S(a)= m(m-1) 2 + k(k-1) 2 -m k .
3. CThen there is an integer x such that for the finite sequence a=(2,3, x, 2 x) , S(a)=-7 .
4. DIf a is a sequence of 100 integers consisting of 2 's and -1 's only then the minimum possible value of S(a) i