Find whole numbers $x$, $y$, $z$, $a$ such that $x^3+y^3+z^3=a^3$
I have got no solution till now.
Please also provide a formula for finding solutions for this equation.
2026-04-01 11:59:24.1775044764
Find whole numbers $x$, $y$, $z$, $a$ such that $x^3+y^3+z^3=a^3$
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Ramanujan gave the integer solutions $$ \begin{align*} x & = 3n^2 + 5nm - 5m^2 \\ y & = 4n^2 - 4nm + 6m^2 \\ z & = 5n^2 - 5nm - 3m^2 \\ w & = 6n^2 - 4nm + 4m^2 \end{align*} $$
for $x^3+y^3+z^3=w^3$. The smallest one is $$ 3^3+4^3+5^3=6^3. $$