MathDB

6

Part of 2005 IMC

Problems(2)

IMC 2005 day 1 pb 6

Source: Peter

7/26/2005
6) GG group, GmG_{m} and GnG_{n} commutative subgroups being the mm and nn th powers of the elements in GG. Prove Ggcd(m,n)G_{gcd(m,n)} is commutative.
group theoryabstract algebraIMCcollege contests
IMC 2005 day 2 pb 6

Source: Peter

7/26/2005
6. If p,q p,q are rationals, r=p+7qr=p+\sqrt{7}q, then prove there exists a matrix (abcd)∈M2(Z)−(±I2)\left(\begin{array}{cc}a&b\\c&d\end{array}\right) \in M_{2}(Z)- ( \pm I_{2}) for which ar+bcr+d=r\frac{ar+b}{cr+d}=r and det(A)=1det(A)=1
linear algebramatrixIMCcollege contests