Question 50
How many nonnegative integer solutions does the equation have
$$
v^{2}+w^{2}+x^{2}+y^{2}+z^{2}=5 ?
$$
By non-negative integer solution we mean an ordered five of non-negative integers $(v, w, x, y, z)$ that satisfy the equation.
Note: two ordered fives that differ even only in the order of the elements (for example, the fives $(1,2,3,4,5)$ and the fives $(3,1,2,4,5))$ are to be considered distinct.
$$
v^{2}+w^{2}+x^{2}+y^{2}+z^{2}=5 ?
$$
By non-negative integer solution we mean an ordered five of non-negative integers $(v, w, x, y, z)$ that satisfy the equation.
Note: two ordered fives that differ even only in the order of the elements (for example, the fives $(1,2,3,4,5)$ and the fives $(3,1,2,4,5))$ are to be considered distinct.