Competition problem — Number theory

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Number theory Difficulty 6.4 National olympiad Prove it

2. After the abstract set of natural numbers $\boldsymbol{N}$ is defined by formula (1) in § 3, prove according to the definitions of addition and multiplication: $\square$
(i) $1+1=2,1+2=3,2+2=4,2+3=5,2+4=3+3=6$ ;
(ii) $2 \cdot 2=4,2 \cdot 3=6,3 \cdot 4=2 \cdot 6=12$ .

Solution

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