Let α be the positive root of the quadratic equation x2=1990x+1. For any m,n∈N, define the operation m∗n=mn+[αm][αn], where [x] is the largest integer no larger than x. Prove that (p∗q)∗r=p∗(q∗r) holds for all p,q,r∈N. quadraticsalgebranumber theory proposednumber theory