Squares of 3...34

Theorem

The following pattern holds:

\(\ds 4^2\)

\(=\)

\(\ds 16\)

\(\ds 34^2\)

\(=\)

\(\ds 1156\)

\(\ds 334^2\)

\(=\)

\(\ds 111 \, 556\)

\(\ds 3334^2\)

\(=\)

\(\ds 11 \, 115 \, 556\)

\(\ds 33334^2\)

\(=\)

\(\ds 1 \, 111 \, 155\, 556\)

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): $3334$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3334$