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Albania IMO TST Problem 4
Albania IMO TST Problem 4
Source:
May 19, 2013
number theory
least common multiple
greatest common divisor
relatively prime
number theory proposed
Problem Statement
Find all couples of natural numbers
(
a
,
b
)
(a,b)
(
a
,
b
)
not relatively prime (
gcd
(
a
,
b
)
≠
1
\gcd(a,b)\neq\ 1
g
cd
(
a
,
b
)
=
1
) such that
gcd
(
a
,
b
)
+
9
lcm
[
a
,
b
]
+
9
(
a
+
b
)
=
7
a
b
.
\gcd(a,b)+9\operatorname{lcm}[a,b]+9(a+b)=7ab.
g
cd
(
a
,
b
)
+
9
lcm
[
a
,
b
]
+
9
(
a
+
b
)
=
7
ab
.
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