| Displaying 1-4 of 4 results found.
page
1
One-half of the x member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for even D(n) = A264354(n).
+20
2
2, 45, 4, 235, 118521, 6, 156, 665, 8, 410581, 1431, 1464, 10, 217061235, 2629, 20578212225, 12, 143681684300109, 88, 4355, 53946009001, 14, 4149148875801021, 244, 6705, 108, 30839304871, 16, 103789115, 78990793279586649, 9775, 2068, 138751721731, 18, 7987764, 2984191388685, 13661, 5246209297401255, 406200, 5142295
COMMENTS
There is only one class of proper solutions for those D = D(n) = A264354(n) that lead to (x1(n), y1(n)) = (x2(n), y2(n)). See A264354 for comments and examples.
The y member of the positive proper fundamental solution (x = x2(n), y = y2(n)) of the second class for the Pell equation x^2 - D(n)*y^2 = +8 for even D(n) = A264354(n).
+20
2
1, 17, 1, 49, 21287, 1, 23, 97, 1, 48727, 161, 151, 1, 21387679, 241, 1826021057, 1, 11692649642023, 7, 337, 3903396217, 1, 294125365483681, 17, 449, 7, 1994828801, 1, 6399911, 4798348971487087, 577, 119, 7867888313, 1, 437071, 161131189369, 721, 273849896195263, 20783, 262759
COMMENTS
There is only one class of proper solutions for those D = D(n) = A264354(n) values leading to (x1(n), y1(n)) = (x2(n), y2(n)).
Odd numbers D not a square that admit proper solutions (x, y) to the Pell equation x^2 - D*y^2 = +8 with both x and y odd.
+10
11
17, 41, 73, 89, 97, 113, 137, 161, 193, 217, 233, 241, 281, 313, 329, 337, 353, 409, 433, 449, 457, 497, 521, 553, 569, 593, 601, 617, 641, 673, 713, 721, 769, 809, 833, 857, 881, 889, 929, 937, 953, 977, 1033, 1049, 1057, 1081, 1097, 1153, 1169, 1193, 1201, 1217, 1241, 1249, 1289, 1321, 1337, 1361, 1409, 1433, 1457, 1481, 1513, 1553, 1561, 1609, 1633, 1649, 1657, 1673, 1697, 1721, 1753, 1777, 1801, 1817, 1841, 1873, 1889, 1913, 1921, 1993
COMMENTS
The case of even D with y odd and x even needs D == 0 (mod 4). See 4* A261246 = A264354 for the even D values that admit proper solutions. There appear one or two classes of solutions in this case.
The values D not a square that admit proper solutions (x, y) to the Pell equation x^2 - D*y^2 = +8, ordered increasingly.
+10
1
8, 17, 28, 41, 56, 73, 89, 92, 97, 113, 124, 136, 137, 161, 184, 188, 193, 217, 233, 241, 248, 281, 284, 313, 316, 329, 337, 353, 376, 392, 409, 412, 433, 449, 457, 476, 497, 508, 521, 553, 568, 569, 593, 601, 604, 617, 632, 641, 668, 673, 713, 721, 764, 769, 776, 796, 809, 824, 833, 857, 881, 889, 892, 929, 937, 952, 953, 956, 977, 1016, 1033, 1049, 1052, 1057, 1081, 1084, 1097, 1148, 1153
COMMENTS
This sequence is the union of A263012 and A264354. See these sequences for details and examples.
Search completed in 0.005 seconds
|