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Division of square nxn into 40x40 and 49x49 squares

Source: Lithuanian TST 2005

April 16, 2005
combinatorics unsolvedcombinatorics

Problem Statement

Find the smallest integer nn such that an n×nn\times n square can be partitioned into 40×4040\times 40 and 49×4949\times 49 squares, with both types of squares present in the partition, if a) 40∣n40|n; b) 49∣n49|n; c) n∈Nn\in \mathbb N.
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