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, 2023

Number theory Difficulty 8.5 Shortlist Prove it Baltic Way

(a) Let $n = 8$ . Determine whether there exists a labelling of an $8 \times 8$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $65$ .

(b) Let $n = 10$ . Determine whether there exists a labelling of a $10 \times 10$ grid such that the following condition is fulfilled: The difference of any two transversal products is always divisible by $101$ .

Solution

See solution of Problem C 3.

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