492 Cubed is Sum of 3 Positive Cubes in 13 Ways/Mistake
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Source Work
- $6$: Number Recreations
- Narcissistic Numbers:
- Miscellaneous
- Narcissistic Numbers:
Mistake
- ... an integer less than $1,000$ whose cube could be represented in $5$ distinct ways as the sum of the cubes of $3$ positive integers...
- In the table below, three solutions to the problem are shown that have gone far beyond ...
- $\begin {array} {ccc}
& n = 492 & \\ a & b & c \\ 24 & 204 & 480 \\ 48 & 85 & 491 \\ 72 & 384 & 396 \\ 113 & 264 & 463 \\ 144 & 360 & 414 \\ 176 & 204 & 472 \\ 207 & 297 & 438 \\ 226 & 332 & 414 \\ 246 & 328 & 410 \\ 281 & 322 & 399 \\ \end {array}$
Correction
The $5$th triple is wrong.
The first number is $114$, not $144$.
Sources
- 1966: Joseph S. Madachy: Mathematics on Vacation ... (previous): $6$: Number Recreations: Narcissistic Numbers: Miscellaneous