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2024 Bangladesh Mathematical Olympiad
P1
Easy diophantine equation
Easy diophantine equation
Source: BdMO 2024 Secondary National P1
March 18, 2024
Diophantine equation
number theory
Divisibility
factorization
Problem Statement
Find all non-negative integers
x
,
y
x, y
x
,
y
such that
x
3
y
+
x
+
y
=
x
y
+
2
x
y
2
x^3y+x+y=xy+2xy^2
x
3
y
+
x
+
y
=
x
y
+
2
x
y
2
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