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(a+1)/b and (b+1)/a are naturals

Source: XII May Olympiad (Olimpiada de Mayo) 2006 L2 P1

September 19, 2022

number theorydivides

Problem Statement

Determine all pairs of natural numbers

a

and

b

such that

\frac{a+1}{b}

and

\frac{b+1}{a}

they are natural numbers.