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no of squares in mxn rectangle, crossed by diagonal (Chile NMO 1989 P2)

Source:

November 19, 2021
geometryrectanglecombinatorics

Problem Statement

We have a rectangle with integer sides m,nm, n that is subdivided into mnmn squares of side 11. Find the number of little squares that are crossed by the diagonal (without counting those that are touched only in one vertex)
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