MathDB
Problems
Contests
National and Regional Contests
Costa Rica Contests
Costa Rica - Final Round
2010 Costa Rica - Final Round
4
4
Part of
2010 Costa Rica - Final Round
Problems
(1)
Two variable diophantine equation
Source: Costa Rica National Olympiad, Final Round, Problem 4
10/14/2011
Find all integer solutions
(
a
,
b
)
(a,b)
(
a
,
b
)
of the equation
(
a
+
b
+
3
)
2
+
2
a
b
=
3
a
b
(
a
+
2
)
(
b
+
2
)
(a+b+3)^2 + 2ab = 3ab(a+2)(b+2)
(
a
+
b
+
3
)
2
+
2
ab
=
3
ab
(
a
+
2
)
(
b
+
2
)
inequalities
number theory unsolved
number theory