Robert Gerbicz wrote: No it can't be equal to 2002. Because: if $ a\geq{10}^{500}$ then $ {a}^{3}\geq{10}^{1500}$ so $ n+m\geq 501+1501>2001$ if $ a<{10}^{500}$ then $ a<{10}^{1500}$ so $ n+m\leq 500+1500<2001$ This proves that $ n+m$ can't be $ 2001$.