Numbers whose Squares are Consecutive Odd or Even Integers Juxtaposed
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Theorem
Integers whose squares consists of $2$ consecutive odd or even integers juxtaposed include:
- $1127^2 = 01 \, 270 \, 129$
- $8874^2 = 78 \, 747 \, 876$
Such integers come in pairs which add to $1$ more than a power of $10$:
- $1127 + 8874 = 10 \, 001$
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Proof
This theorem requires a proof. 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. |
Historical Note
Numbers with this property were reported on by Victor Thébault, in volume $13$ of Scripta Mathematica.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $1127$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $1127$