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National and Regional Contests
Ukraine Contests
Official Ukraine Selection Cycle
Ukraine National Mathematical Olympiad
2021 Ukraine National Mathematical Olympiad
11.5
11.5
Part of
2021 Ukraine National Mathematical Olympiad
Problems
(1)
m^m+ n^n=k^k
Source: 2021 Ukraine NMO 11.6
4/4/2021
Are there natural numbers
(
m
,
n
,
k
)
(m,n,k)
(
m
,
n
,
k
)
that satisfy the equation
m
m
+
n
n
=
k
k
m^m+ n^n=k^k
m
m
+
n
n
=
k
k
?
Diophantine equation
diophantine
number theory