MathDB
2013 HMMT Team #5: Homogeneously Divisible by 2013

Source:

March 27, 2013
HMMT

Problem Statement

Thaddeus is given a 2013×20132013 \times 2013 array of integers each between 11 and 20132013, inclusive. He is allowed two operations:
1. Choose a row, and subtract 11 from each entry.
2. Chooses a column, and add 11 to each entry.
He would like to get an array where all integers are divisible by 20132013. On how many arrays is this possible?
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