Numbers whose Product with Reverse are Equal
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Theorem
- $651 \times 156 = 372 \times 273$
Proof
| \(\ds 651 \times 156\) | \(=\) | \(\ds \paren {3 \times 7 \times 31} \times \paren {2^2 \times 3 \times 13}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 2^2 \times 3^2 \times 7 \times 13 \times 31\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds \paren {2^2 \times 3 \times 31} \times \paren {3 \times 7 \times 13}\) | ||||||||||||
| \(\ds \) | \(=\) | \(\ds 372 \times 273\) |
$\blacksquare$
Historical Note
According to David Wells in his Curious and Interesting Numbers of $1986$, this result appeared in a $1939$ issue of Scripta Mathematica, attributed to A.A.K. Iyangar.
However, it has not been possible to corroborate this.
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $651$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $651$