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Romanian Masters of Mathematics Collection
2023 Romanian Master of Mathematics
1
Funny Diophantine
Funny Diophantine
Source: 2023 RMM, Problem 1
March 1, 2023
number theory
prime numbers
RMM 2023
Diophantine equation
Problem Statement
Determine all prime numbers
p
p
p
and all positive integers
x
x
x
and
y
y
y
satisfying
x
3
+
y
3
=
p
(
x
y
+
p
)
.
x^3+y^3=p(xy+p).
x
3
+
y
3
=
p
(
x
y
+
p
)
.
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