OFFSET
1,2
COMMENTS
Computed from Perron's table (see reference p. 108, for n = 1..28) which gives the minimal x,y values for the Diophantine eq. x^2 - x*y - ((D(n)-1)/4)*y^2= +1, resp., -1 if D(n)=A077425(n), resp, D(n)=A077425(n) and D(n) also in A077426 (this second case excludes in Perron's table the D values with a 'Teilnenner' in brackets).
The conversion from the x,y values of Perron's table to the minimal a=a(n) and b=b(n) solutions is a(n)=2*x(n)-y(n) and b(n)=y(n). If D(n)=A077425(n) is not in A077426 then the equation with -4 has no solution and a(n) and b(n) are the minimal solutions of the a(n)^2 - D(n)*b(n)^2 = +4 equation. If D(n)=A077425(n) is in A077426 then the a(n) and b(n) values are the minimal solution of the a(n)^2 - D(n)*b(n)^2 = -4 equation. In this case a(+,n)= a(n)^2+2 and b(+,n)=a(n)*b(n) are the minimal solution of a^2 - D(n)*b^2 = +4.
REFERENCES
O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108).
EXAMPLE
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Nov 29 2002
EXTENSIONS
More terms from Matthew Conroy, Apr 20 2003
STATUS
approved