MathDB

2

Part of 1987 China Team Selection Test

Problems(2)

closed recticular polygon

Source: China TST 1987, problem 2

5/16/2005
A closed recticular polygon with 100 sides (may be concave) is given such that it's vertices have integer coordinates, it's sides are parallel to the axis and all it's sides have odd length. Prove that it's area is odd.
analytic geometrygeometryinductiongeometry unsolvedPolygonscoordinatesChina
x^3+y^3+z^3=nx^2y^2z^2

Source: China TST 1987, problem 5

5/16/2005
Find all positive integer nn such that the equation x3+y3+z3=n⋅x2⋅y2⋅z2x^3+y^3+z^3=n \cdot x^2 \cdot y^2 \cdot z^2 has positive integer solutions.
LaTeXnumber theory unsolvednumber theory