Triplet in Arithmetic Sequence with equal Sigma
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This theorem requires a proof.
It remains to be shown that these are the smallest.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
Theorem
The smallest triple of integers in arithmetic sequence which have the same $\sigma$ (sigma) value is:
- $\map \sigma {267} = \map \sigma {295} = \map \sigma {323} = 360$
Proof
We have that:
| \(\ds 295 - 267\) | \(=\) | \(\ds 28\) | ||||||||||||
| \(\ds 323 - 295\) | \(=\) | \(\ds 28\) |
demonstrating that $267, 295, 323$ are in arithmetic sequence with common difference $28$.
Then:
| \(\ds \map \sigma {267}\) | \(=\) | \(\ds 360\) | $\sigma$ of $267$ | |||||||||||
| \(\ds \map \sigma {295}\) | \(=\) | \(\ds 360\) | $\sigma$ of $295$ | |||||||||||
| \(\ds \map \sigma {323}\) | \(=\) | \(\ds 360\) | $\sigma$ of $323$ |
It remains to be shown that these are the smallest.
You can help $\mathsf{Pr} \infty \mathsf{fWiki}$ by crafting such a proof.
When this page/section has been completed, {{ProofWanted}} should be removed from the code.
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Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $267$