

A226702


Positive solutions y/5 of the Pell equation x^2  61*y^2 = 4.


1



1, 1522, 2318005, 3530320093, 5376675183634, 8188672774354489, 12471343258666703113, 18993847594276614486610, 28927617414740025196403917, 44056742328801464097508678981, 67098389639147215080480521684146
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OFFSET

0,2


COMMENTS

The proper and improper positive solutions of the Pell equation x^2  61*y^2 = 4 are x = 39*A226701(n) and y = 5*a(n), n >= 1.


REFERENCES

T. Nagell, Introduction to Number Theory, Chelsea Publishing Company, New York, 1964, ch. Vi, 58., p. 204212.


LINKS



FORMULA

a(n) = S(n,1523)  S(n1,1523), n >= 0, with the Chebyshev Spolynomials (A049310), where S(1,x) = 0.
O.g.f.: (1  x)/(1  1523*x + x^2).
a(n) = 1523*a(n1)  a(n2), n>=1, a(1) = 1, a(0) = 1.


MATHEMATICA

LinearRecurrence[{1523, 1}, {1, 1522}, 20] (* Harvey P. Dale, Aug 03 2014 *)


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



