I know if $x_1 + x_2 + x_3 + x_4 \leq k$ then number of integral solution can be given by ${k + 4} \choose 4$ using Stars and Bars but I am unable to figure out no. of integral solutions of $x_1 + x_2^2 + x_3^3 + x_4^4 \leq k$. where $ 0\leq x_1, x_2 ,x_3, x_4 \leq 10^3 $ and $0 \leq k \leq 10^{18}$. Kindly help.
2026-03-29 20:45:37.1774817137
Number of non negative integral solutions involving exponents
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