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H.R end 14308 48749 a 14308 49605 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (theorem.3) cvn H.B /ANN pdfmark end 14308 49605 a Black Fn(,)535 b(it)514 b(is)h(easy)g(to)g(establish)g(the)f(follo)-36 b(wing)516 b(prop)36 b(erties)514 b(of)i(the)d(p)36 b(olynomials)800 51210 y(and)433 b(zeros:)2751 53444 y(1.)579 b Fm(S)5141 53643 y Fr(n)5767 53444 y Fn(\()p Fk(\000)p Fm(x)p Fn(\))369 b(=)f Fm(S)11100 53643 y Fr(n)11727 53444 y Fn(\()p Fm(x)p Fn(\))433 b(for)h Fm(n)369 b Fk(\025)h Fn(2)p Fm(;)434 b Fn(and)f(if)h Fm(r)405 b Fk(2)369 b(Z)26821 53643 y Fr(n)27880 53444 y Fn(then)433 b Fk(\000)p Fm(r)405 b Fk(2)369 b(Z)35085 53643 y Fr(n)36145 53444 y Fn(for)434 b Fm(n)369 b Fk(\025)g Fn(1)p Fm(:)2751 55049 y Fn(2.)579 b Fm(x)5080 54567 y Fq(2)5550 54254 y Fd(n)p Fc(\000)p Fb(1)7218 55049 y Fm(S)8018 55248 y Fr(n)8644 55049 y Fn(\(1)p Fm(=x)p Fn(\))369 b(=)g Fm(S)14245 55248 y Fr(n)14871 55049 y Fn(\()p Fm(x)p Fn(\))433 b(for)h Fm(n)370 b Fk(\025)f Fn(3)p Fm(;)434 b Fn(and)f(if)i Fm(r)405 b Fk(2)368 b(Z)29965 55248 y Fr(n)31025 55049 y Fn(then)432 b(1)p Fm(=r)406 b Fk(2)369 b(Z)38497 55248 y Fr(n)39556 55049 y Fn(for)435 b Fm(n)369 b Fk(\025)g Fn(2)p Fm(:)2751 56654 y Fn(3.)641 b(Supp)36 b(ose)454 b(that)g Fm(c)404 b(>)g Fn(0)p Fm(;)455 b Fn(and)f(let)h Fm(r)21247 56853 y Fr(n)22328 56654 y Fn(denote)f(the)g(greatest)g(zero)h(of)g Fm(S)38811 56853 y Fr(n)39438 56654 y Fm(:)f Fn(Then)g(\()p Fm(r)44762 56853 y Fr(n)45389 56654 y Fn(\))g(is)h(a)f(strictly)800 58259 y(increasing)434 b(sequence,)g(and)16085 61781 y(lim)15762 62578 y Fr(n)p Fj(!1)18215 61781 y Fm(r)18801 61980 y Fr(n)19796 61781 y Fn(=)21177 59908 y Ff(\032)22726 60978 y Fn(\(1)296 b Fk(\000)f Fm(c)p Fn(\))26572 60496 y Fj(\000)p Fq(1)p Fr(=)p Fq(2)28770 60978 y Fm(;)1108 b Fn(if)434 b(0)369 b Fm(<)g(c)g(<)f Fn(1;)25084 62584 y Fk(1)p Fm(;)3466 b Fn(if)434 b Fm(c)369 b Fk(\025)g Fn(1)p Fm(:)800 65595 y Fn(An)340 b(outline)g(of)h(a)f(pro)36 b(of)341 b(follo)-36 b(ws.)549 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Fm(S)34411 3200 y Fq(4)34334 4077 y Fr(n)p Fj(\000)p Fq(2)36163 3749 y Fm(:)13964 b Fn(\(12\))800 6073 y(T)-108 b(o)434 b(pro)-36 b(v)g(e)433 b(this)h(recurrence,)f(from)h(\()p 0 .5 0 TeXcolorrgb 18981 6073 a SDict begin H.S end 18981 6073 a 0 .5 0 TeXcolorrgb Fn(5)p 0 .5 0 TeXcolorrgb 19631 5217 a SDict begin H.R end 19631 5217 a 19631 6073 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.5) cvn H.B /ANN pdfmark end 19631 6073 a Black Fn(\))f(w)-36 b(e)434 b(obtain)g(b)36 b(oth)15938 9007 y Fm(c)16498 8458 y Fq(2)p Fr(n)p Fj(\000)p Fq(4)18796 9007 y Fn(\()p Fm(S)20102 9206 y Fq(1)20628 9007 y Fm(S)21428 9206 y Fq(2)22175 9007 y Fk(\001)221 b(\001)g(\001)h Fm(S)24746 9206 y Fr(n)p Fj(\000)p Fq(3)26575 9007 y Fn(\))27081 8458 y Fq(2)27606 9007 y Fm(S)28483 8458 y Fq(2)28406 9335 y Fr(n)p Fj(\000)p Fq(2)30604 9007 y Fn(=)368 b Fm(S)32861 8458 y Fq(2)32784 9335 y Fr(n)p Fj(\000)p Fq(1)34908 9007 y Fk(\000)295 b Fm(S)37036 9206 y Fr(n)800 11940 y Fn(and)16470 13545 y Fm(c)17030 12997 y Fq(2)p Fr(n)p Fj(\000)p Fq(6)19329 13545 y Fn(\()p Fm(S)20635 13744 y Fq(1)21160 13545 y Fm(S)21960 13744 y Fq(2)22707 13545 y Fk(\001)221 b(\001)g(\001)i Fm(S)25279 13744 y Fr(n)p Fj(\000)p Fq(3)27107 13545 y Fn(\))27613 12997 y Fq(2)28508 13545 y Fn(=)368 b Fm(S)30765 12997 y Fq(2)30688 13874 y Fr(n)p Fj(\000)p Fq(2)32812 13545 y Fk(\000)295 b Fm(S)34940 13744 y Fr(n)p Fj(\000)p Fq(1)36769 13545 y Fm(;)800 15870 y Fn(and)433 b(\()p 0 .5 0 TeXcolorrgb 3835 15870 a SDict begin H.S end 3835 15870 a 0 .5 0 TeXcolorrgb Fn(12)p 0 .5 0 TeXcolorrgb 5136 15014 a SDict begin H.R end 5136 15014 a 5136 15870 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.12) cvn H.B /ANN pdfmark end 5136 15870 a Black Fn(\))g(follo)-36 b(ws)435 b(b)-36 b(y)434 b(eliminating)g(\()p Fm(S)20250 16069 y Fq(1)20776 15870 y Fm(S)21576 16069 y Fq(2)22323 15870 y Fk(\001)221 b(\001)g(\001)h Fm(S)24894 16069 y Fr(n)p Fj(\000)p Fq(3)26723 15870 y Fn(\))27229 15388 y Fq(2)27754 15870 y Fm(:)2751 17475 y Fn(In)516 b(the)f(case)h Fm(c)508 b Fn(=)h(1)p Fm(;)516 b Fn(the)f(recurrence)g(\()p 0 .5 0 TeXcolorrgb 22929 17475 a SDict begin H.S end 22929 17475 a 0 .5 0 TeXcolorrgb Fn(12)p 0 .5 0 TeXcolorrgb 24229 16619 a SDict begin H.R end 24229 16619 a 24229 17475 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.12) cvn H.B /ANN pdfmark end 24229 17475 a Black Fn(\))h(is)g(used)f(\(e.g.,)537 b([)p 0 .5 0 TeXcolorrgb 33408 17475 a SDict begin H.S end 33408 17475 a 0 .5 0 TeXcolorrgb Fn(1)p 0 .5 0 TeXcolorrgb 34059 16619 a SDict begin H.R end 34059 16619 a 34059 17475 a SDict begin [ /Color [0 1 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (cite.Mon) cvn H.B /ANN pdfmark end 34059 17475 a Black Fn(]\))516 b(to)f(de\014ne)g(the)g(Gor)-69 b(\024)-582 b(sk)-36 b(o)g(v-Wirsing)800 19080 y(p)36 b(olynomials,)399 b(for)388 b(whic)-36 b(h)388 b(the)f(initial)i(p)36 b(olynomials)389 b(are)f(2)p Fm(x)202 b Fk(\000)g Fn(1)388 b(and)g(5)p Fm(x)36927 18598 y Fq(2)37655 19080 y Fk(\000)202 b Fn(5)p Fm(x)g Fn(+)g(1)387 b(rather)g(than)h Fm(x)g Fn(and)800 20685 y Fm(x)1539 20203 y Fq(2)2360 20685 y Fk(\000)296 b Fn(1)p Fm(:)800 22798 y SDict begin H.S end 800 22798 a 800 22798 a SDict begin 14.5 H.A end 800 22798 a 800 22798 a SDict begin [ /View [/XYZ H.V] /Dest (section.3) cvn H.B /DEST pdfmark end 800 22798 a 2324 x Fo(3)2152 b(The)716 b(p)60 b(olynomials)715 b Fi(V)21448 25409 y Fm(n)22811 25122 y Fh(=)532 b Fi(S)25872 25409 y Fm(n)27128 25122 y Fg(\000)425 b Fi(c)29847 24428 y Fm(n)p Fk(\000)p Fn(1)32363 25122 y Fi(S)33515 25409 y Fn(1)34220 25122 y Fi(S)35372 25409 y Fn(2)36397 25122 y Fg(\001)319 b(\001)g(\001)g Fi(S)40099 25409 y Fm(n)p Fk(\000)p Fn(1)800 28043 y(Equation)409 b(\()p 0 .5 0 TeXcolorrgb 6899 28043 a SDict begin H.S end 6899 28043 a 0 .5 0 TeXcolorrgb Fn(5)p 0 .5 0 TeXcolorrgb 7549 27187 a SDict begin H.R end 7549 27187 a 7549 28043 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.5) cvn H.B /ANN pdfmark end 7549 28043 a Black Fn(\))f(sho)-36 b(ws)409 b(that)e Fm(n)370 b Fk(\025)f Fn(2)p Fm(;)409 b Fn(the)f(p)36 b(olynomial)410 b Fm(S)28644 28242 y Fr(n)p Fq(+1)30880 28043 y Fn(factors.)g(W)-108 b(e)408 b(use)g(one)g(of)i(factors)f(to)f(de\014ne)800 29648 y(a)434 b(sequence)f(of)i(p)36 b(olynomials)15554 28043 y SDict begin H.S end 15554 28043 a 15554 28043 a SDict begin 14.5 H.A end 15554 28043 a 15554 28043 a SDict begin [ /View [/XYZ H.V] /Dest (equation.13) cvn H.B /DEST pdfmark end 15554 28043 a 16255 32581 a Fm(V)17013 32780 y Fr(n)18008 32581 y Fn(=)369 b Fm(V)20147 32780 y Fr(n)20773 32581 y Fn(\()p Fm(x)p Fn(\))g(=)g Fm(S)25074 32780 y Fr(n)25995 32581 y Fk(\000)295 b Fm(c)27883 32033 y Fr(n)p Fj(\000)p Fq(1)29712 32581 y Fm(S)30512 32780 y Fq(1)31037 32581 y Fm(S)31837 32780 y Fq(2)32585 32581 y Fk(\001)221 b(\001)g(\001)h Fm(S)35156 32780 y Fr(n)p Fj(\000)p Fq(1)36984 32581 y Fm(;)13143 b Fn(\(13\))800 35515 y(so)434 b(that)18778 38448 y SDict begin H.S end 18778 38448 a 18778 38448 a SDict begin 14.5 H.A end 18778 38448 a 18778 38448 a SDict begin [ /View [/XYZ H.V] /Dest (equation.14) cvn H.B /DEST pdfmark end 18778 38448 a Fm(S)19578 38647 y Fr(n)20205 38448 y Fn(\()p Fm(x)p Fn(\))1106 b(=)h Fm(V)25939 38647 y Fr(n)p Fj(\000)p Fq(1)27768 38448 y Fn(\()p Fm(x)p Fn(\))p Fm(V)30277 38647 y Fr(n)p Fj(\000)p Fq(1)32105 38448 y Fn(\()p Fk(\000)p Fm(x)p Fn(\))p Fm(;)p Black 15238 w Fn(\(14\))p Black 18128 40385 a(2)p Fm(S)19578 40584 y Fr(n)20205 40385 y Fn(\()p Fm(x)p Fn(\))f(=)h Fm(V)25939 40584 y Fr(n)26565 40385 y Fn(\()p Fm(x)p Fn(\))295 b(+)g Fm(V)30676 40584 y Fr(n)31303 40385 y Fn(\()p Fk(\000)p Fm(x)p Fn(\))p Fm(:)p Black 16040 w Fn(\(15\))p Black 800 43319 a(Supp)36 b(ose)385 b(that)i Fm(n)369 b Fk(\025)g Fn(3)p Fm(:)387 b Fn(Substitute)e Fm(n)199 b Fk(\000)g Fn(1)387 b(for)g Fm(n)g Fn(in)g(\()p 0 .5 0 TeXcolorrgb 27142 43319 a SDict begin H.S end 27142 43319 a 0 .5 0 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(cite.Rah) cvn H.B /ANN pdfmark end 1812 8564 a Black Fn(,)434 b(pp.)f(196{209].)800 10894 y SDict begin H.S end 800 10894 a 800 10894 a SDict begin 14.5 H.A end 800 10894 a 800 10894 a SDict begin [ /View [/XYZ H.V] /Dest (section.6) cvn H.B /DEST pdfmark end 800 10894 a 2103 x Fo(6)2152 b(The)716 b(case)i Fi(c)531 b Fh(=)g(2)p Fi(i)800 15918 y Fn(Supp)36 b(ose)433 b(that)g Fm(S)9520 16117 y Fr(n)10579 15918 y Fn(is)h(a)g(square)g(for)g(some)g Fm(n;)g Fn(and)f(write)h Fm(S)30531 16117 y Fr(n)31157 15918 y Fn(\()p Fm(x)p Fn(\))369 b(=)g Fm(H)35839 15436 y Fq(2)35736 16246 y Fr(n)36364 15918 y Fn(\()p Fm(x)p Fn(\))p Fm(:)434 b Fn(Then)18974 19418 y Fm(S)19774 19617 y Fr(n)20400 19418 y Fn(\()21039 18520 y Fm(x)p 21039 19113 740 54 v 21129 20329 a(c)22206 19418 y Fk(\000)23991 18520 y Fn(1)p 23667 19113 1299 54 v 23667 20329 a Fm(cx)25099 19418 y Fn(\))369 b(=)f Fm(H)28535 18870 y Fq(2)28432 19747 y Fr(n)29060 19418 y Fn(\()29699 18520 y Fm(x)p 29699 19113 740 54 v 29789 20329 a(c)30866 19418 y Fk(\000)32652 18520 y Fn(1)p 32327 19113 1299 54 v 32327 20329 a Fm(cx)33759 19418 y Fn(\))p Fm(:)800 22739 y Fn(By)434 b(\()p 0 .5 0 TeXcolorrgb 3347 22739 a SDict begin H.S end 3347 22739 a 0 .5 0 TeXcolorrgb Fn(9)p 0 .5 0 TeXcolorrgb 3997 21883 a SDict begin H.R end 3997 21883 a 3997 22739 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.9) cvn H.B /ANN pdfmark end 3997 22739 a Black Fn(\),)4864 21134 y SDict begin H.S end 4864 21134 a 4864 21134 a SDict begin 14.5 H.A end 4864 21134 a 4864 21134 a SDict begin [ /View [/XYZ H.V] /Dest (equation.20) cvn H.B /DEST pdfmark end 4864 21134 a 17876 24937 a Fm(S)18676 25136 y Fr(n)p Fq(+1)20504 24937 y Fn(\()p Fm(x)p Fn(\))369 b(=)f(\()p Fm(cx)p Fn(\))26315 24388 y Fq(2)26785 24076 y Fd(n)p Fc(\000)p Fb(1)28453 24937 y Fm(H)29634 24388 y Fq(2)29531 25265 y Fr(n)30159 24937 y Fn(\()30798 24038 y Fm(x)p 30798 24631 740 54 v 30888 25848 a(c)31965 24937 y Fk(\000)33750 24038 y Fn(1)p 33426 24631 1299 54 v 33426 25848 a Fm(cx)34857 24937 y Fn(\))p Fm(;)14764 b Fn(\(20\))800 27590 y(whic)-36 b(h)403 b(implies)h(that)f Fm(S)12464 27789 y Fr(n)p Fq(+1)14695 27590 y Fn(is)h(a)g(square.)568 b(It)404 b(is)f(easy)h(to)g(sho)-36 b(w)403 b(that)g(the)g(only)h(nonzero)f(c) -36 b(hoices)403 b(of)h Fm(c)f Fn(for)800 29195 y(whic)-36 b(h)433 b Fm(S)5321 29394 y Fq(3)6281 29195 y Fn(is)h(a)f(square)h(are) g Fk(\006)p Fn(2)p Fm(i)p Fn(.)1012 b(Equation)434 b(\()p 0 .5 0 TeXcolorrgb 24554 29195 a SDict begin H.S end 24554 29195 a 0 .5 0 TeXcolorrgb Fn(20)p 0 .5 0 TeXcolorrgb 25855 28339 a SDict begin H.R end 25855 28339 a 25855 29195 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.20) cvn H.B /ANN pdfmark end 25855 29195 a Black Fn(\))f(giv)-36 b(es)435 b(the)e(recurrence)17203 32710 y Fm(H)18281 32909 y Fr(n)p Fq(+1)20110 32710 y Fn(\()p Fm(x)p Fn(\))368 b(=)h(\(2)p Fm(ix)p Fn(\))26455 32161 y Fq(2)26925 31849 y Fd(n)p Fc(\000)p Fb(2)28593 32710 y Fm(H)29671 32909 y Fr(n)30297 32710 y Fn(\()31408 31811 y Fm(i)p 30936 32404 1390 54 v 30936 33621 a Fn(2)p Fm(x)32753 32710 y Fk(\000)34214 31811 y Fm(ix)p 34214 32404 1183 54 v 34480 33621 a Fn(2)35530 32710 y(\))p Fm(;)800 35957 y Fn(whic)-36 b(h)433 b(implies)17921 36433 y Ff(\014)17921 37230 y(\014)18364 37562 y Fm(H)19442 37761 y Fr(n)p Fq(+1)21270 37562 y Fn(\()p Fm(e)22379 37014 y Fr(i\022)23219 37562 y Fn(\))23725 36433 y Ff(\014)23725 37230 y(\014)24537 37562 y Fn(=)368 b(2)26567 37014 y Fq(deg)171 b Fr(H)28922 37125 y Fd(n)29765 37562 y Fk(j)p Fm(H)31212 37761 y Fr(n)31838 37562 y Fn(\(sin)221 b Fm(\022)37 b Fn(\))p Fk(j)800 39876 y Fn(for)434 b(all)h(real)f Fm(\022)36 b(:)434 b Fn(Another)f(recurrence,)f(whic)-36 b(h)434 b(follo)-36 b(ws)435 b(readily)g(from)f(\()p 0 .5 0 TeXcolorrgb 36170 39876 a SDict begin H.S end 36170 39876 a 0 .5 0 TeXcolorrgb Fn(12)p 0 .5 0 TeXcolorrgb 37470 39020 a SDict begin H.R end 37470 39020 a 37470 39876 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.12) cvn H.B /ANN pdfmark end 37470 39876 a Black Fn(\),)g(is)20849 42784 y Fm(H)21927 42983 y Fr(n)22922 42784 y Fn(=)369 b(2)p Fm(H)26134 42235 y Fq(4)26031 43112 y Fr(n)p Fj(\000)p Fq(2)28155 42784 y Fk(\000)295 b Fm(H)30664 42235 y Fq(2)30561 43112 y Fr(n)p Fj(\000)p Fq(1)32389 42784 y Fm(:)800 45692 y Fn(The)434 b(\014rst)e(four)i(of)g(these)g(p)36 b(olynomials)435 b(are)f(as)f(follo)-36 b(ws:)2751 47954 y Fm(H)3829 48153 y Fq(3)4355 47954 y Fn(\()p Fm(x)p Fn(\))368 b(=)h Fm(x)8594 47472 y Fq(2)9415 47954 y Fn(+)295 b(1)2751 49559 y Fm(H)3829 49758 y Fq(4)4355 49559 y Fn(\()p Fm(x)p Fn(\))368 b(=)h Fm(x)8594 49077 y Fq(4)9415 49559 y Fk(\000)295 b Fn(6)p Fm(x)12132 49077 y Fq(2)12954 49559 y Fn(+)g(1)2751 51164 y Fm(H)3829 51363 y Fq(5)4355 51164 y Fn(\()p Fm(x)p Fn(\))368 b(=)h Fm(x)8594 50682 y Fq(8)9415 51164 y Fn(+)295 b(20)p Fm(x)12761 50682 y Fq(6)13583 51164 y Fk(\000)g Fn(26)p Fm(x)16950 50682 y Fq(4)17772 51164 y Fn(+)g(20)p Fm(x)21118 50682 y Fq(2)21939 51164 y Fn(+)g(1)2751 52769 y Fm(H)3829 52968 y Fq(6)4355 52769 y Fn(\()p Fm(x)p Fn(\))368 b(=)h Fm(x)8594 52287 y Fq(16)9885 52769 y Fk(\000)296 b Fn(88)p Fm(x)13253 52287 y Fq(14)14545 52769 y Fn(+)f(92)p Fm(x)17891 52287 y Fq(12)19183 52769 y Fk(\000)g Fn(872)p Fm(x)23200 52287 y Fq(10)24493 52769 y Fn(+)g(1990)p Fm(x)29139 52287 y Fq(8)29961 52769 y Fk(\000)h Fn(872)p Fm(x)33979 52287 y Fq(6)34801 52769 y Fn(+)f(92)p Fm(x)38147 52287 y Fq(4)38968 52769 y Fk(\000)h Fn(88)p Fm(x)42336 52287 y Fq(2)43157 52769 y Fn(+)f(1)2751 55031 y(Co)36 b(e\016cien)-36 b(ts)434 b(for)g(the)f(p)36 b(olynomials)435 b Fm(H)22233 55230 y Fq(7)23192 55031 y Fn(and)f Fm(H)26800 55230 y Fq(8)27759 55031 y Fn(are)f(giv)-36 b(en)435 b(at)p 0 1 0 0 TeXcolorcmyk 34912 55297 a SDict begin H.S end 34912 55297 a 0 1 0 0 TeXcolorcmyk -266 x Fn(A154308)p 34912 55243 4878 54 v 0 1 0 0 TeXcolorcmyk 39789 54123 a SDict begin H.R end 39789 54123 a 39789 55031 a SDict begin [ /H /I /Border [0 0 0] /Color [0 1 1] /Action << /Subtype /URI /URI (http://www.research.att.com/cgi-bin/access.cgi/as/~njas/sequences/eisA.cgi?Anum=A154308) >> /Subtype /Link H.B /ANN pdfmark end 39789 55031 a Black Fn(.)800 57294 y SDict begin H.S end 800 57294 a 800 57294 a SDict begin 14.5 H.A end 800 57294 a 800 57294 a SDict begin [ /View [/XYZ H.V] /Dest (section.7) cvn H.B /DEST pdfmark end 800 57294 a 2170 x Fo(7)2152 b(The)716 b(recurrence)h Fi(P)20230 59751 y Fm(n)p Fn(+1)22724 59464 y Fi(=Q)25143 59751 y Fm(n)p Fn(+1)28169 59464 y Fh(=)531 b(\(1)p Fi(=c)p Fh(\)\()p Fi(P)35934 59751 y Fm(n)36768 59464 y Fi(=Q)39187 59751 y Fm(n)40445 59464 y Fh(+)425 b Fi(Q)43730 59751 y Fm(n)44562 59464 y Fi(=P)46705 59751 y Fm(n)47537 59464 y Fh(\))800 62385 y Fn(W)-108 b(e)620 b(return)e(no)-36 b(w)620 b(to)g(the)f(recurrence)g(\()p 0 .5 0 TeXcolorrgb 21463 62385 a SDict begin H.S end 21463 62385 a 0 .5 0 TeXcolorrgb Fn(1)p 0 .5 0 TeXcolorrgb 22113 61529 a SDict begin H.R end 22113 61529 a 22113 62385 a SDict begin [ /Color [1 0 0] /H /I /Border [0 0 0] /Subtype /Link /Dest (equation.1) cvn H.B /ANN pdfmark end 22113 62385 a Black Fn(\),)666 b(with)620 b(initial)g(v)-72 b(alue)620 b Fm(x)35023 62584 y Fq(0)36235 62385 y Fn(=)686 b Fm(P)38771 62584 y Fq(1)39982 62385 y Fn(=)g Fm(P)42518 62584 y Fq(1)43044 62385 y Fn(\()p Fm(x)p Fn(\))g(=)f Fm(x:)620 b Fn(T)-108 b(aking)800 63990 y Fm(Q)1830 64189 y Fq(1)2725 63990 y Fn(=)369 b Fm(Q)5136 64189 y Fq(1)5662 63990 y Fn(\()p Fm(x)p Fn(\))f(=)h(1)434 b(leads)g(to)f(sequences)h Fm(P)21836 64189 y Fr(n)22896 63990 y Fn(and)f Fm(Q)26455 64189 y Fr(n)27515 63990 y Fn(de\014ned)f(b)-36 b(y)14074 67200 y Fm(P)14912 67399 y Fr(n)15908 67200 y Fn(=)369 b Fm(P)18308 66651 y Fq(2)18127 67528 y Fr(n)p Fj(\000)p Fq(1)20251 67200 y Fn(+)295 b Fm(cQ)23148 66651 y Fq(2)23148 67528 y Fr(n)p Fj(\000)p Fq(1)26277 67200 y Fn(and)1300 b Fm(Q)30703 67399 y Fr(n)31698 67200 y Fn(=)369 b Fm(cP)34477 67399 y Fr(n)p Fj(\000)p Fq(1)36306 67200 y Fm(Q)37336 67399 y Fr(n)p 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