Solutions to Approximate Fermat Equation x^3 = y^3 + z^3 Plus or Minus 1/Mistake
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Source Work
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $729$
Mistake
Mistake $1$:
- $9^3$ and the $2$nd smallest cube to be the sum of $3$ cubes: $9^3 = 1^3 + 6^3 + 8^3$. This makes $7^3$ the smallest solution to the approximate Fermat equation, $x^3 = y^3 + z^3 + 1$.
Mistake $2$:
- The next such solution is $104^3 = 64^3 + 94^3 + 1$.
The first mistake is that it is not $7^3$ but $9^3$ which is the solution to that equation.
The second mistake is that $104^3 = 64^3 + 94^3 - 1$.
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $729$