"페르마의 두 제곱의 합에 대한 정리"의 두 판 사이의 차이

2009년 11월 2일 (월) 18:30 판

두 정수 \(x,y\)에 대하여 \(x^2+y^2\) 형태로 표현될 수 있는 소수 \(p\)에 대한 문제
\(p=2\) 또는 \(p \equiv 1 \pmod 4\) 이면 모두 적당한 정수 \(x,y\)에 대하여 \(x^2+y^2\) 형태로 표현가능

0, 1, 2, 4, 5, 8, 9, 10, 13, 16, 17, 18, 20, 25, 26, 29, 32, 34, 36, 37, 40, 41, 45, 49, 50, 52, 53, 58, 61, 64, 65, 68, 72, 73, 74, 80, 81, 82, 85, 89, 90, 97, 98, 100, 101, 104, 106, 109, 113, 116, 117, 121, 122, 125, 128, 130, 136, 137, 144, 145, 146, 148, 149, 153, 157, 160, 162, 164, 169, 170, 173, 178, 180, 181, 185, 193, 194, 196, 197, 200, 202, 205, 208, 212, 218, 221, 225, 226, 229, 232, 233, 234, 241, 242, 244, 245, 250, 256, 257, 260, 261, 265, 269, 272, 274, 277, 281, 288, 289, 290, 292, 293, 296, 298, 305, 306, 313, 314, 317, 320, 324, 325, 328, 333, 337, 338, 340, 346, 349, 353, 356, 360, 361, 362, 365, 369, 370, 373, 377, 386, 388, 389, 392, 394, 397, 400

2, 5, 13, 17, 29, 37, 41, 53, 61, 73, 89, 97, 101, 109, 113, 137, 149, 157, 173, 181, 193, 197, 229, 233, 241, 257, 269, 277, 281, 293, 313, 317, 337, 349, 353, 373, 389, 397

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397

\(x^2+2y^2\)로 표현되는 소수

2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193, 211, 227, 233, 241, 251, 257, 281, 283, 307, 313, 331, 337, 347, 353, 379

\(x^2+3y^2\)

3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397

\(x^2+5y^2\)

@@ 35번째 줄: / 35번째 줄: @@
 *  2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397<br>
+<math>x^2+2y^2</math>로 표현되는 소수
+*  2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193, 211, 227, 233, 241, 251, 257, 281, 283, 307, 313, 331, 337, 347, 353, 379<br>
+<math>x^2+3y^2</math>
+*  3, 7, 13, 19, 31, 37, 43, 61, 67, 73, 79, 97, 103, 109, 127, 139, 151, 157, 163, 181, 193, 199, 211, 223, 229, 241, 271, 277, 283, 307, 313, 331, 337, 349, 367, 373, 379, 397<br>
+<math>x^2+5y^2</math>
+*  5, 29, 41, 61, 89, 101, 109, 149, 181, 229, 241, 269, 281, 349, 389<br>