The Pellian Equation x2 −Dy2 = 1 from Multiple Sequences
(Part XFb)

This article is a continuation of Part XFa and tabulates the results correponding to the sequences Pb(n) and P(m).

Pell Equal Expressions for (x,936,1) Triples

Table II [Pb(n)]
Pell EquationEqual Expressions
x2 − 41923y2 = 1 R41923 = (2662 + 13√41923 + 288×74)2 ∕74 = 191647 + 936√41923
x2 − 69300y2 = 1 R69300 = (3422 + 13√69300 − 288×95)2 ∕95 = 246011 + 936√69300
x2 − 452594y2 = 1 R452594 = (8746 + 13√452594 + 288×243)2 ∕243 = 629695 + 936√452594
x2 − 534725y2 = 1 R534725 = (9506 + 13√534725 − 288×264)2 ∕264 = 684449 + 936√534725
x2 − 1301313y2 = 1 R1301313 = (14830 + 13√1301313 + 288×412)2 ∕412 = 1067743 + 936√1301313
x2 − 1438198y2 = 1 R1438198 = (15590 + 13√1438198 − 288×433)2 ∕433 = 1122497 + 936√1438198
x2 − 2588080y2 = 1 R2588080 = (20914 + 13√2588080 + 288×581)2 ∕581 = 1505791 + 936√2588080
x2 − 2779719y2 = 1 R2779719 = (21674 + 13√2779719 − 288×602) 2 ∕602 = 1560545 + 936√2779719
x2 − 4312895y2 = 1 R4312895 = (26998 + 13√4312895 + 288×750)2 ∕750 = 1943839 + 936√4312895
x2 − 4559288y2 = 1 R4559288 = (27758 + 13√4559288 − 288×771)2 ∕771 = 1998593 + 936√4559288
x2 − 6475758y2 = 1 R6475758 = (33082 + 13√6475758 + 288×919)2 ∕919 = 2381887 + 936√6475758
x2 − 6776905y2 = 1 R6776905 = (33842 + 13√6776905 − 288×940)2 ∕940 = 2436641 + 936√6776905
Table III [P(m)]
Pell EquationEqual Expressions
x2 − 219023y2 = 1 R219023 = (468 + √219023)2 = 438047 + 936√219023
x2 − 219025y2 = 1 R219025 = (468 + √219025)2 = 438049 + 936√219025
x2 − 876094y2 = 1 R219025 = (936 + √876094)2 ∕2 = 876095 + 936√876094
x2 − 876098y2 = 1 R876098 = (936 + √876098)2 ∕2 = 876097 + 936√876098
x2 − 1971213y2 = 1 R1971213 = (1404 + √1971213)2 ∕3 = 1314143 + 936√1971213
x2 − 1971219y2 = 1 R1971219 = (1404 + √1971219)2 ∕3 = 1314145 + 936√1971219
x2 − 3504380y2 = 1 R3504380 = (1872 + √3504380)2 ∕4 = 1752191 + 936√3504380
x2 − 3504388y2 = 1 R3504388 = (1872 + √3504388)2 ∕4 = 1752193 + 936√3504388
x2 − 5475595y2 = 1 R5475595 = (2340 + √5475595)2 ∕5 = 2190239 + 936√5475595
x2 − 5475605y2 = 1 R5475605 = (2340 + √5475605)2 ∕5 = 2190241 + 936√5475605
x2 − 7884858y2 = 1 R7884858 = (2808 + √7884858)2 ∕6 = 2628287 + 936√7884858
x2 − 7884870y2 = 1 R7884870 = (2808 + √7884870)2 ∕6 = 2628289 + 936√7884870

This concludes Part XFb. Go back to Part XFa.

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