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Balkan MO
2019 Balkan MO
1
1
Part of
2019 Balkan MO
Problems
(1)
Function with primes
Source: BMO 2019, Problem 1
5/2/2019
Let
P
\mathbb{P}
P
be the set of all prime numbers. Find all functions
f
:
P
→
P
f:\mathbb{P}\rightarrow\mathbb{P}
f
:
P
→
P
such that:
f
(
p
)
f
(
q
)
+
q
p
=
f
(
q
)
f
(
p
)
+
p
q
f(p)^{f(q)}+q^p=f(q)^{f(p)}+p^q
f
(
p
)
f
(
q
)
+
q
p
=
f
(
q
)
f
(
p
)
+
p
q
holds for all
p
,
q
∈
P
p,q\in\mathbb{P}
p
,
q
∈
P
.Proposed by Dorlir Ahmeti, Albania
function
number theory
prime numbers