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2023 German National Olympiad
1
1
Part of
2023 German National Olympiad
Problems
(1)
Diophantine equation in two variables with 2023
Source: Germany 2023, Problem 1
6/16/2023
Determine all pairs
(
m
,
n
)
(m,n)
(
m
,
n
)
of integers with
n
≥
m
n \ge m
n
≥
m
satisfying the equation
n
3
+
m
3
−
n
m
(
n
+
m
)
=
2023.
n^3+m^3-nm(n+m)=2023.
n
3
+
m
3
−
nm
(
n
+
m
)
=
2023.
number theory
Diophantine equation
number theory proposed
algebra proposed