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A130226 Smallest integer x satisfying the Pell equation x^2-ny^2=-1 for the values of n given in A031396. 5
0, 1, 2, 3, 18, 4, 5, 70, 6, 32, 7, 182, 99, 29718, 8, 1068, 43, 9, 378, 500, 5604, 10, 4005, 8890182, 776, 11, 682, 57, 1744, 12, 113582, 4832118, 13, 1118, 1111225770, 68, 1764132, 14, 3141, 251, 15, 1710, 23156, 71011068, 4443, 16, 6072, 82, 1407 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

K Lakshmi, R Someshwari On The Negative Pell Equation y^2 = 72x^2 - 23, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 7, July (2016).

S Vidhyalakshmi, V Krithika, K Agalya, On The Negative Pell Equation, International Journal of Emerging Technologies in Engineering Research (IJETER), Volume 4, Issue 2, February (2016) www.ijeter.everscience.org,

LINKS

Ray Chandler, Table of n, a(n) for n = 1..10000

R. Suganya, D. Maheswari, On the Negative Pellian Equation y^2 = 110 * x^2 - 29, Journal of Mathematics and Informatics, Vol. 11 (2017), pp. 63-71.

MAPLE

A130226 := proc(m)

    local xm, x , i, xmo, y2;

    xm := [] ; # x^2-m*y^2=-1 (mod m) requires x in xm[]

    for x from 0 to m-1 do

        if modp(x^2, m) = modp(-1, m) then

            xm := [op(xm), x] ;

        end if;

    end do:

    for i from 0 do

        for xmo in xm do

            x := i*m+xmo ;

            y2 := (x^2+1)/m ;

            if issqr(y2) then

                return x ;

            end if;

        end do:

    end do:

end proc:

L := BFILETOLIST("b031396.txt") ;

n := 1:

for m in L do

    printf("%d %d\n", n, A130226(m)) ;

    n := n+1 ;

end do: # R. J. Mathar, Oct 19 2014

CROSSREFS

Cf. A094048.

Sequence in context: A263048 A118702 A073524 * A287621 A032808 A321212

Adjacent sequences:  A130223 A130224 A130225 * A130227 A130228 A130229

KEYWORD

nonn

AUTHOR

Colin Barker, Aug 05 2007

STATUS

approved

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Last modified March 25 10:31 EDT 2019. Contains 321470 sequences. (Running on oeis4.)