MathDB

33

Part of 1977 IMO Longlists

Problems(1)

For every vector there is a scalar n [ILL 1977]

Source:

1/11/2011
A circle KK centered at (0,0)(0,0) is given. Prove that for every vector (a1,a2)(a_1,a_2) there is a positive integer nn such that the circle KK translated by the vector n(a1,a2)n(a_1,a_2) contains a lattice point (i.e., a point both of whose coordinates are integers).
vectoranalytic geometrygeometry unsolvedgeometry