Difference between Two Squares equal to Repunit/Examples/R 2
Jump to navigation
Jump to search
Example of Difference between Two Squares equal to Repunit
We have that $11$ is a prime.
\(\ds 11\) | \(=\) | \(\ds 1 \times 11\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds \frac {11 + 1} 2\) | \(=\) | \(\ds 6\) | |||||||||||
\(\ds \frac {11 - 1} 2\) | \(=\) | \(\ds 5\) | ||||||||||||
\(\ds \leadsto \ \ \) | \(\ds 6^2 - 5^2\) | \(=\) | \(\ds 36 - 25\) | |||||||||||
\(\ds \) | \(=\) | \(\ds 11\) |
$\blacksquare$
Sources
- Dec. 1986: C.B. Lacampagne and J.L. Selfridge: Pairs of Squares with Consecutive Digits (Math. Mag. Vol. 59, no. 5: pp. 270 – 275) www.jstor.org/stable/2689401
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $2025$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $2025$