# Cube of 71 is Odd Integers in Sequence

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## Theorem

The cube of $71$, when expressed in decimal notation, is the odd integers from $3$ to $11$ written in sequence:

- $71^3 = 357 \, 911$

## Proof

Verified by direct calculation.

## Historical Note

The interesting phenomenon that $71^3$ consists of the odd integers from $3$ to $11$ in sequence is reported by David Wells in *Curious and Interesting Numbers* as being noted by a contributor to *Journal of Recreational Mathematics* called **James Davies**, writing in Volume $13$.

An online listing of the articles for that journal has revealed an article titled *An Evening With Pi* by James Davis, but further investigation will need to be done to establish the exact nature of this.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $71$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $71$