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.
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J. W. Tanner
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What did you try? – Jan 12 '20 at 19:24
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Please use MathJax to format your question. – Jan 12 '20 at 19:25
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1Why did you tag this question ‘linear algebra’? – J. W. Tanner Jan 12 '20 at 19:27
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Formula how to find solutions – Sonalisa Borkar Jan 12 '20 at 19:27
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3Why would you expect this to be straight forward? In general, the sum of three cubes problem is extremely difficult. – lulu Jan 12 '20 at 19:28
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1Fully answered here: https://math.stackexchange.com/questions/1118456/can-the-cube-of-every-perfect-number-be-written-as-the-sum-of-three-cubes . – Eric Towers Jan 12 '20 at 19:31
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Does this answer your question? Can the cube of every perfect number be written as the sum of three cubes? – Dietrich Burde Jan 12 '20 at 19:49
1 Answers
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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 $$ 3^3+4^3+5^3=6^3. $$
Dietrich Burde
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