Blanche's Dissection divides a square into 7 noncongruent rectangles of the same area. Seven is the minimum possible.
That solution uses non-integer values. What is the smallest non-trivial solution where all rectangles have integer sides?
For example, can a $360\times360$ square be divided into different rectangles all with the same area?
EDIT: mathoverflow has Tiling a square with rectangles. There and at Blanche Dissections I outline a solution method. The method was used to find these 16 non-integer equidissections of a square.
