Sum of 2 Squares in 2 Distinct Ways/Sequence
Jump to navigation
Jump to search
Theorem
The sequence of positive integers which can be expressed as the sum of two square numbers in two or more different ways begins:
\(\ds 50\) | \(=\) | \(\ds 7^2 + 1^2\) | \(\ds = 5^2 + 5^2\) | |||||||||||
\(\ds 65\) | \(=\) | \(\ds 8^2 + 1^2\) | \(\ds = 7^2 + 4^2\) | |||||||||||
\(\ds 85\) | \(=\) | \(\ds 9^2 + 2^2\) | \(\ds = 7^2 + 6^2\) | |||||||||||
\(\ds 125\) | \(=\) | \(\ds 11^2 + 2^2\) | \(\ds = 10^2 + 5^2\) | |||||||||||
\(\ds 130\) | \(=\) | \(\ds 11^2 + 3^2\) | \(\ds = 9^2 + 7^2\) | |||||||||||
\(\ds 145\) | \(=\) | \(\ds 12^2 + 1^2\) | \(\ds = 9^2 + 8^2\) | |||||||||||
\(\ds 170\) | \(=\) | \(\ds 13^2 + 1^2\) | \(\ds = 11^2 + 7^2\) |
This sequence is A007692 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $50$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $50$