How many integer solutions are there to the equation x1+x2+x3=0 if x1, x2, x3 > - 5?

x1+x2+x3=0 if x1, x2, x3 > - 5?

and the solutions are integer

x1 = - 4 and x2+x3=4 we count (-4; 4; 0), (-4; 0; 4), (-4; 3; 1), (-4; 1; 3), (-4; 2; 2), (-4; 2; 2)

x1 = - 3 and x2+x3=3 we count (-3; 0; 3), (-3; 3; 0), (-3; 1; 2), (-3; 2; 1)

x1 = - 2 and x2+x3=2 we count (-2; 0; 2). (-2; 2; 0), (-2; 1; 1)

x1 = - 1 and x2+x3=1 we count (-1; 0; 1), (-1; 1; 0)

x1=0 and (0; 0; 0), (0; 1; -1), (0; -1; 1)

There are 42 solutions

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