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2005 CentroAmerican
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Easy diophantine equation
Source: VII Centroamerican and Caribbean Olympiad 2005, Problem 2
7/29/2005
Show that the equation
a
2
b
2
+
b
2
c
2
+
3
b
2
−
c
2
−
a
2
=
2005
a^{2}b^{2}+b^{2}c^{2}+3b^{2}-c^{2}-a^{2}=2005
a
2
b
2
+
b
2
c
2
+
3
b
2
−
c
2
−
a
2
=
2005
has no integer solutions. Arnoldo Aguilar, El Salvador
number theory proposed
number theory