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How is the atomic number of an atom determined?

How is the atomic number of an atom determined?

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How many integer solutions are there to the equation
x1 + x2 + 2x3 + x4 + x5 = 72
when
(a) xi 0,i = 1,...,5
(b) xi 1,i = 1,...,5

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How is the atomic number of an atom determined?

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