Problem 1.
An integer n>1 is called if there exists a permutation a₁,a₂,a₃,...,a_n of the numbers 1,2,3,...,n , such that:
(i) a_i and a_i+1 have different parities for every 1 ≤ i ≤n-1 ;
(ii)  the sum a₁+a₂+a₃+...+a_k  is a quadratic residue modulo n  for every 1 ≤ k ≤n  .
Prove that there exist infinitely many good numbers, as well as infinitely many positive integers which are not good.