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no 1 to 16 written in a squared 4x4 paper with divisible sums by n

Source: Mexican Mathematical Olympiad 1996 OMM P4

July 28, 2018
combinatoricsnumber theorySum

Problem Statement

For which integers n≥2n\ge 2 can the numbers 11 to 1616 be written each in one square of a squared 4×44\times 4 paper such that the 88 sums of the numbers in rows and columns are all different and divisible by nn?
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