Sum of 2 Squares in 2 Distinct Ways/Sequence

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): $50$