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Easy diophantine equation

Source: VII Centroamerican and Caribbean Olympiad 2005, Problem 2

July 29, 2005
number theory proposednumber theory

Problem Statement

Show that the equation a2b2+b2c2+3b2−c2−a2=2005a^{2}b^{2}+b^{2}c^{2}+3b^{2}-c^{2}-a^{2}=2005 has no integer solutions. Arnoldo Aguilar, El Salvador
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