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A161583
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The list of the k values in the common solutions to the 2 equations 15*k+1=A^2, 19*k+1=B^2.
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3
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0, 17, 4896, 1405152, 403273745, 115738159680, 33216448554432, 9533004996962321, 2735939217679631712, 785205022469057339040, 225351105509401776672785, 64674982076175840847750272, 18561494504756956921527655296, 5327084247883170460637589319697
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OFFSET
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1,2
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COMMENTS
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The 2 equations are equivalent to the Pell equation x^2-285*y^2=1,
with x=(285*k+17)/2 and y=A*B/2, case C=15 in A160682.
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LINKS
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FORMULA
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k(t+3)=288*(k(t+2)-k(t+1))+k(t).
k(t)=((17+w)*((287+17*w)/2)^(t-1)+(17-w)*((287-17*w)/2)^(t-1))/570 where w=sqrt(285).
k(t) = floor of ((17+w)*((287+17*w)/2)^(t-1))/570;
G.f.: -17*x^2/((x-1)*(x^2-287*x+1)).
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MAPLE
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t:=0: for n from 0 to 1000000 do a:=sqrt(15*n+1): b:=sqrt(19*n+1):
if (trunc(a)=a) and (trunc(b)=b) then t:=t+1: print(t, n, a, b): end if: end do:
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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