Problem of the Week

This problem was suggested by Professor Mary Jane Sterling of Bradley University. Many thanks for the kickoff of the semester!

Take a checkerboard with n rows and m columns, with n and m relatively prime (i.e., having no common factors). Through how many squares does a line going from one corner of the board to the opposite corner pass?  For example, a diagonal on a 3 ´ 5 checkerboard passes though 7 squares.

(Your answer should be a function of the two variables n and m.  Please explain your answer completely.  To start with, why should n and m be relatively prime?)

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ã2002 Alberto L. Delgado