2

Part of 2015 VJIMC

Problems(2)

VJIMC 2015 Category I, Problem 2

Source: VJIMC2015

Problem 2 Consider the infinite chessboard whose rows and columns are indexed by positive integers. Is it possible to put a single positive rational number into each cell of the chessboard so that each positive rational number appears exactly once and the sum of every row and of every column is finite?

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VJIMC 2015 Category II, Problem 2

Source: VJIMC2015

Problem 2 Determine all pairs

(n, m)

of positive integers satisfying the equation

5^n = 6m^2 + 1\ .

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