MathDB
Problems
Contests
National and Regional Contests
Greece Contests
Greece Junior Math Olympiad
2001 Greece Junior Math Olympiad
2
Number Theory
Number Theory
Source: Archimedes Junior 2001
March 17, 2020
number theory
Problem Statement
(a) Find all pairs
(
m
,
n
)
(m, n)
(
m
,
n
)
of integers satisfying
m
3
−
4
m
n
2
=
8
n
3
−
2
m
2
n
m^3-4mn^2=8n^3-2m^2n
m
3
−
4
m
n
2
=
8
n
3
−
2
m
2
n
(b) Among such pairs find those for which
m
+
n
2
=
3
m+n^2=3
m
+
n
2
=
3
Back to Problems
View on AoPS