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National and Regional Contests
Iran Contests
Iran MO (2nd Round)
2013 Iran MO (2nd Round)
1
a/b = a.b
a/b = a.b
Source: Iran second round- 2013- P1
May 4, 2013
number theory proposed
number theory
Problem Statement
Find all pairs
(
a
,
b
)
(a,b)
(
a
,
b
)
of positive integers for which
gcd
(
a
,
b
)
=
1
\gcd(a,b)=1
g
cd
(
a
,
b
)
=
1
, and
a
b
=
b
.
a
‾
\frac{a}{b}=\overline{b.a}
b
a
=
b
.
a
. (For example, if
a
=
92
a=92
a
=
92
and
b
=
13
b=13
b
=
13
, then
b
/
a
=
13.92
b/a=13.92
b
/
a
=
13.92
)
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