A mod-dot product between two arrays with length n produce a new array with length n. If array A is a1,a2,...,an and array B is b1,b2,...bn, then A mod-dot B produce an array C c1,c2,...,cn such that c1 = a1*b1%n, c2 = a2*b2%n,...,ci = ai*bi%n,..., cn = an*bn%n.
i.e. A = [2,3,4] and B = [5,2,2] then A mod-dot B = [1,0,2].
A permutation of n is an array with length n and every number from 0 to n-1 appears in the array by exactly one time.
i.e. A = [2,0,1] is a permutation of 3, and B = [3,4,1,2,0] is a permutation of 5, but C = [1,2,2,3] is NOT a permutation of 4.
Now comes the problem: Are there two permutaion of n such that their mod-dot product is also a permutation of n?