MathDB

1

Part of 1995 South africa National Olympiad

Problems(2)

Quadratic Diophantine equation with no solutions

Source: South African MO 1995 Q1

5/27/2012
Prove that there are no integers mm and nn such that 19m2+95mn+2000n2=1995.19m^2+95mn+2000n^2=1995.
quadraticsnumber theory unsolvednumber theory
Find the area of the larger quadrilateral

Source: South African MO 1995 Q5

5/27/2012
The convex quadrilateral ABCDABCD has area 11, and ABAB is produced to EE, BCBC to FF, CDCD to GG and DADA to HH, such that AB=BEAB=BE, BC=CFBC=CF, CD=DGCD=DG and DA=AHDA=AH. Find the area of the quadrilateral EFGHEFGH.
geometrygeometry unsolved