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2018 Macedonia JBMO TST
4
2018 JBMO TST- Macedonia, problem 4
2018 JBMO TST- Macedonia, problem 4
Source: 2018 JBMO TST- Macedonia
May 28, 2019
Junior
Macedonia
JMMO
2018
number theory
Problem Statement
Determine all pairs
(
p
,
q
)
(p, q)
(
p
,
q
)
,
p
,
q
∈
N
p, q \in \mathbb {N}
p
,
q
∈
N
, such that
(
p
+
1
)
p
−
1
+
(
p
−
1
)
p
+
1
=
q
q
(p + 1)^{p - 1} + (p - 1)^{p + 1} = q^q
(
p
+
1
)
p
−
1
+
(
p
−
1
)
p
+
1
=
q
q
.
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