Three Tri-Automorphic Numbers for each Number of Digits/Examples/10 Digits
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Examples of Three Tri-Automorphic Numbers for each Number of Digits
The $3$ tri-automorphic numbers with $10$ digits are:
\(\text {(6 666 666 667)}: \quad\) | \(\ds 3 \times 6 \, 666 \, 666 \, 667^2\) | \(=\) | \(\ds 133 \, 333 \, 333 \, 34 \mathbf {6 \, 666 \, 666 \, 667}\) | |||||||||||
\(\text {(7 262 369 792)}: \quad\) | \(\ds 3 \times 7 \, 262 \, 369 \, 792^2\) | \(=\) | \(\ds 158 \, 226 \, 044 \, 98 \mathbf {7 \, 262 \, 369 \, 792}\) | |||||||||||
\(\text {(9 404 296 875)}: \quad\) | \(\ds 3 \times 9 \, 404 \, 296 \, 875^2\) | \(=\) | \(\ds 265 \, 322 \, 399 \, 13 \mathbf {9 \, 404 \, 296 \, 875}\) |
Historical Note
According to David Wells in his $1997$ book Curious and Interesting Numbers, 2nd ed., this result is attributed to J.A.H. Hunter, in volume $5$ of the Journal of Recreational Mathematics.
No online corroboration of this can be found online, as there appears to be no consolidated archive of this magazine.
The author of this page would give his right arm to have a copy of the entire series resting on a bookshelf in his study.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $6667$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6667$