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a/b is written in the decimal system as b.a, find a and b

Source: 4-th Hungary-Israel Binational Mathematical Competition 1993

May 26, 2007

quadraticsnumber theory proposednumber theory

Problem Statement

Find all pairs of coprime natural numbers

a

and

b

such that the fraction

\frac{a}{b}

is written in the decimal system as

b.a.