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.

Blanche Dissections

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    $\begingroup$ A square is a rectangle, is it not? The answer would seem to be 1. $\endgroup$ – Jens Aug 9 '16 at 19:18
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    $\begingroup$ @Jens Haha, very funny. I think nontrivial dissections are a reasonable assumption. $\endgroup$ – heropup Aug 9 '16 at 19:23
  • $\begingroup$ Do you know of at least one such dissection? They seem rather difficult to construct. $\endgroup$ – Pierre-Guy Plamondon Aug 11 '16 at 12:45

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