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A142955
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Primes of the form 3*x^2 + 4*x*y - 5*y^2 (as well as of the form 3*x^2 + 10*x*y + 2*y^2).
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1
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2, 3, 19, 31, 59, 67, 71, 79, 103, 107, 127, 151, 167, 179, 211, 223, 227, 307, 331, 379, 383, 431, 439, 487, 523, 547, 563, 599, 607, 659, 683, 743, 751, 787, 811, 827, 839, 863, 887, 907, 911, 971, 983, 991, 1019, 1039, 1063, 1091, 1123, 1171, 1231, 1283
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OFFSET
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1,1
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COMMENTS
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Discriminant = 76. Class = 2. Binary quadratic forms a*x^2 + b*x*y + c*y^2 have discriminant d = b^2 - 4ac.
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REFERENCES
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Z. I. Borevich and I. R. Shafarevich, Number Theory.
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LINKS
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EXAMPLE
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a(4) = 31 because we can write 31 = 3*3^2 + 4*3*2 - 5*2^2 (or 31 = 3*1^2 + 10*1*2 + 2*2^2).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Laura Caballero Fernandez, Lourdes Calvo Moguer, Maria Josefa Cano Marquez, Oscar Jesus Falcon Ganfornina and Sergio Garrido Morales (laucabfer(AT)alum.us.es), Jul 14 2008
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EXTENSIONS
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STATUS
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approved
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