Squares of 23...3

Theorem

The following pattern holds:

\(\ds 3^2\)

\(=\)

\(\ds 9\)

\(\ds 23^2\)

\(=\)

\(\ds 529\)

\(\ds 233^2\)

\(=\)

\(\ds 54 \, 289\)

\(\ds 2333^2\)

\(=\)

\(\ds 5 \, 442 \, 889\)

\(\ds 23333^2\)

\(=\)

\(\ds 544 \, 428 \, 889\)

and so on.

Proof

This theorem requires a proof. In particular: Simple but tedious. You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{ProofWanted}} from the code. If you would welcome a second opinion as to whether your work is correct, add a call to {{Proofread}} the page.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2333$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2333$