MathDB
Lattice

Source: Iranian National Olympiad (3rd Round) 2006

August 26, 2006
abstract algebragroup theorycalculusintegrationinvariantnumber theory proposednumber theory

Problem Statement

LL is a fullrank lattice in R2\mathbb R^{2} and KK is a sub-lattice of LL, that A(K)A(L)=m\frac{A(K)}{A(L)}=m. If mm is the least number that for each x∈Lx\in L, mxmx is in KK. Prove that there exists a basis {x1,x2}\{x_{1},x_{2}\} for LL that {x1,mx2}\{x_{1},mx_{2}\} is a basis for KK.
Back to ProblemsView on AoPS