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A068717
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a(n) = -1 if A067280(n) == 0 (mod 2), otherwise a(n) = A049240(n).
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4
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0, -1, 1, 0, -1, 1, 1, 1, 0, -1, 1, 1, -1, 1, 1, 0, -1, 1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 0, -1, 1, 1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, 1, 0, -1, 1, 1, -1, 1, 1, 1, -1, 1, 1, 1, 1, 1
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OFFSET
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1,1
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COMMENTS
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Previous name was: x*x - n*y*y = +-1 has infinitely many solutions in integers (x,y).
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REFERENCES
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H. Davenport, The Higher Arithmetic. Cambridge Univ. Press, 7th ed., 1999, table 1.
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LINKS
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FORMULA
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EXAMPLE
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a(2)= -1: x*x - 2*y*y = -1 is soluble, e.g., 7*7 - 2*5*5 = -1.
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PROG
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(Python)
from math import isqrt
from sympy import continued_fraction_periodic
def A068717(n): return 0 if (a:=isqrt(n)**2==n) else (-1 if len(continued_fraction_periodic(0, 1, n)[1]) & 1 else 1-int(a)) # Chai Wah Wu, Jun 14 2022
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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