MathDB
Binary Operation(star) - ILL 1990 IRE3

Source:

September 18, 2010
quadraticsalgebranumber theory proposednumber theory

Problem Statement

Let α\alpha be the positive root of the quadratic equation x2=1990x+1x^2 = 1990x + 1. For any m,n∈Nm, n \in \mathbb N, define the operation m∗n=mn+[αm][αn]m*n = mn + [\alpha m][ \alpha n], where [x][x] is the largest integer no larger than xx. Prove that (p∗q)∗r=p∗(q∗r)(p*q)*r = p*(q*r) holds for all p,q,r∈N.p, q, r \in \mathbb N.
Back to ProblemsView on AoPS