Primes Expressible as x^2 + n y^2 for all n from 1 to 10/Examples/1129
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Example of Prime Expressible as $x^2 + n y^2$ for all $n$ from $1$ to $10$
\(\ds 1129\) | \(=\) | \(\ds 20^2 + 1 \times 27^2 = 27^2 + 1 \times 20^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 29^2 + 2 \times 12^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 19^2 + 3 \times 16^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 27^2 + 4 \times 10^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 2^2 + 5 \times 15^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 23^2 + 6 \times 10^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 11^2 + 7 \times 12^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 29^2 + 8 \times 6^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 20^2 + 9 \times 9^2\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds 33^2 + 10 \times 2^2\) |