MathDB

Initially, a pair of numbers

(1,1)

is written on the board. If for some

x

and

y

one of the pairs

(x, y-1)

and

(x+y, y+1)

is written on the board, then you can add the other one. Similarly for

(x, xy)

and

(\frac {1} {x}, y)

. Prove that for each pair that appears on the board, its first number will be positive.

Problem Statement