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Balkan MO
2024 Balkan MO
3
3
Part of
2024 Balkan MO
Problems
(1)
number theory, divisibility, inequality
Source: BMO 2024 Problem 3
4/29/2024
Let
a
a
a
and
b
b
b
be distinct positive integers such that
3
a
+
2
3^a + 2
3
a
+
2
is divisible by
3
b
+
2
3^b + 2
3
b
+
2
. Prove that
a
>
b
2
a > b^2
a
>
b
2
.Proposed by Tynyshbek Anuarbekov, Kazakhstan
number theory
Divisibility
Inequality
inequalities