Problems(1)
Given a finite sequence x1,1,x2,1,…,xn,1 of integers (n≥2), not all equal, define the sequences x1,k,…,xn,k by
x_{i,k+1}=\frac{1}{2}(x_{i,k}+x_{i+1,k}) \text{where }x_{n+1,k}=x_{1,k}.
Show that if n is odd, then not all xj,k are integers. Is this also true for even n? algebra unsolvedalgebra