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Kyiv City MO
2023 Kyiv City MO
2023 Kyiv City MO Round 1
Problem 3
NT for beginners
NT for beginners
Source: Kyiv City MO 2023 7.3
May 14, 2023
number theory
Problem Statement
Prove that there don't exist positive integer numbers
k
k
k
and
n
n
n
which satisfy equation
n
n
+
(
n
+
1
)
n
+
1
+
(
n
+
2
)
n
+
2
=
202
3
k
n^n+(n+1)^{n+1}+(n+2)^{n+2} = 2023^k
n
n
+
(
n
+
1
)
n
+
1
+
(
n
+
2
)
n
+
2
=
202
3
k
. Proposed by Mykhailo Shtandenko
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