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Number of solutions of equation

Source: 40th Austrian Mathematical Olympiad 2009, round 1, problem 2

August 5, 2009
combinatorics proposedcombinatorics

Problem Statement

How many integer solutions (x0 (x_0, x1 x_1, x2 x_2, x3 x_3, x4 x_4, x5 x_5, x6) x_6) does the equation 2x_0^2\plus{}x_1^2\plus{}x_2^2\plus{}x_3^2\plus{}x_4^2\plus{}x_5^2\plus{}x_6^2\equal{}9 have?
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