Square of Reversal of Small-Digit Number

Theorem

Let $n$ be an integer whose decimal representation consists of sufficiently small digits.

Then the reversal of the square of $n$ is the square of the reversal of $n$.


Proof


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Examples

Square of Reversal of $12$

$12^2 = 144$
$21^2 = 441$


Square of Reversal of $13$

$13^2 = 169$
$31^2 = 961$


Sources

  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $12$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $12$
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