有一个真分数7/a它的前N位的之和是1949求a和N

真分数 7/a=0.xxxxxxxx.....，从第一个数字0开始到第N位，数值之和为1949，对应的a和N是多少？

有许多答案。未经严格证明，试算结果看，应该有无数组。

在 8≤a≤2000 范围搜索，有316组答案。每个括号内为一组 (a,N)。

第一组为例，(13,434) 表示 a=13，N=434。即：

7/13=0.5384615384615384615384615384615 ......

0+5+3+8+4+6+1+5+3 .... 一共434位数字之和为1949

附：316组答案和fortran代码

(13,434)；(17,435)；(30,651)；(33,1300)；(43,413)；(57,436)；(61,435)；(76,434)；(81,409)；(86,454)；(94,433)；(97,444)；(107,411)；(115,434)；(121,434)；(124,542)；(130,435)；(132,1298)；(137,435)；(144,1936)；(163,430)；(170,436)；(178,436)；(184,434)；(192,648)；(206,436)；(208,435)；(218,436)；(225,1949)；(258,456)；(263,433)；(269,431)；(288,394)；(292,436)；(293,433)；(295,436)；(296,328)；(298,436)；(300,652)；(303,1300)；(304,437)；(307,444)；(309,404)；(311,499)；(321,438)；(330,1301)；(332,468)；(333,1950)；(346,468)；(352,433)；(353,435)；(361,439)；(363,459)；(379,435)；(383,439)；(384,329)；(388,442)；(395,404)；(401,441)；(416,434)；(421,434)；(423,434)；(430,414)；(432,587)；(445,434)；(446,437)；(453,400)；(457,435)；(461,434)；(466,431)；(475,436)；(478,508)；(481,652)；(482,436)；(489,432)；(493,452)；(494,436)；(507,428)；(515,435)；(517,434)；(519,413)；(533,468)；(537,441)；(538,438)；(543,435)；(563,445)；(570,437)；(572,437)；(610,436)；(618,473)；(621,432)；(624,330)；(628,441)；(629,415)；(641,435)；(648,466)；(652,431)；(669,438)；(683,422)；(689,434)；(692,424)；(709,438)；(713,439)；(723,409)；(724,430)；(725,435)；(741,391)；(744,543)；(751,421)；(755,399)；(758,438)；(760,435)；(769,439)；(779,435)；(785,440)；(795,531)；(796,470)；(797,424)；(804,421)；(807,437)；(808,435)；(810,410)；(813,650)；(818,436)；(832,437)；(834,405)；(835,437)；(843,481)；(860,455)；(872,435)；(883,428)；(887,461)；(888,327)；(912,433)；(914,437)；(926,437)；(932,435)；(934,422)；(940,434)；(942,396)；(944,437)；(970,445)；(971,420)；(974,428)；(978,442)；(979,436)；(982,440)；(996,436)；(1005,449)；(1007,435)；(1035,419)；(1053,440)；(1056,264)；(1058,432)；(1069,426)；(1070,412)；(1074,431)；(1077,430)；(1079,416)；(1087,439)；(1096,435)；(1098,431)；(1101,430)；(1112,432)；(1116,492)；(1132,443)；(1133,430)；(1136,365)；(1138,444)；(1139,439)；(1142,435)；(1144,435)；(1150,435)；(1151,471)；(1163,434)；(1165,434)；(1171,439)；(1173,464)；(1181,440)；(1182,486)；(1195,382)；(1203,448)；(1206,469)；(1207,418)；(1210,435)；(1212,328)；(1214,438)；(1216,432)；(1217,432)；(1221,652)；(1226,463)；(1235,436)；(1240,543)；(1241,580)；(1254,490)；(1266,466)；(1273,442)；(1299,436)；(1300,436)；(1308,436)；(1311,408)；(1313,868)；(1314,559)；(1320,1299)；(1322,435)；(1325,405)；(1327,431)；(1328,469)；(1329,432)；(1332,490)；(1339,438)；(1345,440)；(1346,433)；(1353,500)；(1355,544)；(1357,422)；(1359,408)；(1362,437)；(1368,435)；(1370,436)；(1374,433)；(1375,436)；(1376,459)；(1392,448)；(1398,434)；(1399,448)；(1403,438)；(1413,413)；(1419,481)；(1426,441)；(1429,435)；(1440,1937)；(1441,435)；(1448,438)；(1453,429)；(1461,425)；(1465,432)；(1466,413)；(1492,438)；(1494,463)；(1504,438)；(1506,423)；(1532,443)；(1548,405)；(1556,434)；(1563,455)；(1567,451)；(1569,452)；(1571,440)；(1574,432)；(1584,394)；(1592,481)；(1599,467)；(1607,432)；(1608,452)；(1611,438)；(1619,442)；(1623,429)；(1629,432)；(1630,431)；(1642,428)；(1643,442)；(1654,445)；(1672,437)；(1674,461)；(1678,466)；(1684,434)；(1691,441)；(1698,428)；(1700,437)；(1706,431)；(1709,435)；(1711,452)；(1712,413)；(1741,439)；(1744,438)；(1745,437)；(1780,437)；(1793,453)；(1795,390)；(1798,448)；(1802,429)；(1811,460)；(1812,401)；(1814,415)；(1815,448)；(1819,441)；(1833,441)；(1836,439)；(1838,421)；(1840,435)；(1842,422)；(1843,420)；(1847,430)；(1851,449)；(1854,401)；(1867,440)；(1868,452)；(1885,436)；(1892,396)；(1894,440)；(1899,489)；(1901,441)；(1902,486)；(1920,649)；(1922,443)；(1923,488)；(1926,445)；(1934,441)；(1935,474)；(1957,419)；(1961,499)；(1963,434)；(1978,438)；(1985,444)；(1986,450)。

total = 316

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